High School
SAT
ACT
University
MCAT
LSAT
DAT

Implicit Differentiation: Tangent line

Related Topics

Wize University Calculus 1 Textbook > Derivatives

Implicit Differentiation

4 Activities

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Find the equation of the tangent to the graph 3y3+x=x2+13y^3+x=x^2+1 at x=2x=2.







More Implicit Differentiation Questions:
Implicit differentiation
Differentiate exy−tan⁡y=3x3+2xe^{xy}-\tan y=\frac{3}{x^3}+2x
Implicit Differentiation: Tangent line
Find the equation of the tangent to the graph 3y3+x=x2+13y^3+x=x^2+1 at x=2x=2.
Tangent lines: Implicit Differentiation
An equation of the tangent line to the curve x3+xln⁡y+y4=3x32+exx^3+x\ln y+y^4=3x^{\frac{3}{2}}+e^x at x=0x=0 is
Implicit Differentiation: Logarithmic Differentiation
Find the equation of the tangent line to
(sin⁡(xy))x=x1/4(\sin(xy))^x = x^{1/4}
at the point (12,π2)\left(\dfrac{1}{2},\dfrac{\pi}{2}\right).
Implicit Second Derivative
Find d2ydx2\dfrac{d^2y}{dx^2} at the point (2,2)(2,2) given xy+y2=2xy+y^2=2
Implicit differentiation
Differentiate exy−tan⁡y=3x3+2xe^{xy}-\tan y=\frac{3}{x^3}+2x
Implicit Differentiation
Find the slope of the line tangent to the curve xy=x3y−6\sqrt{xy}=x^3y-6 at the point (1,9).
Tangent lines: Implicit Differentiation
An equation of the tangent line to the curve x3+xln⁡y+y4=3x32+exx^3+x\ln y+y^4=3x^{\frac{3}{2}}+e^x at x=0x=0 is
Implicit Differentiation
Find y'' if x3+y3=4.x^3+y^3=4.
Implicit Differentiation
Find dydx\displaystyle \frac{\text{d}y}{\text{d}x} for y3=2xy^3=2x.
Implicit Differentiation
Find the slope of the line tangent to the curve xy=x3y−6\sqrt{xy}=x^3y-6 at the point (1,9).
Implicit differentiation
Find the derivative of the following:
yex+y2=x2ye^{x+y^2}=x^2
Tangent lines: Implicit Differentiation
An equation of the tangent line to the curve x3+xln⁡y+y4=3x32+exx^3+x\ln y+y^4=3x^{\frac{3}{2}}+e^x at x=0x=0 is
Find the tangent to the curve 4𝑦2 − 𝑒𝑥 + 𝑥 = 4𝑥 + 3 at the point where 𝑥 = 0 and 𝑦 is positive
Implicit Differentiation
Evaluate the slope of the line tangent to the curve xy=x3y−6\sqrt{xy}=x^3y-6 at the point P(1,9)P(1,9).
Implicit Differentiation: Tangent line
Find the equation of the tangent to the graph 3y3+x=x2+13y^3+x=x^2+1 at x=2x=2.
Implicit Differentiation
Evaluate the slope of the line tangent to the curve xy=x3y−6\sqrt{xy}=x^3y-6 at the point P(1,9)P(1,9).
Implicit Differentiation
For the implicit equation x4+x3y−xy2=1x^4+x^3y-xy^2=1, where y = f(x), find y'.
Implicit Differentiation: Tangent line
Find the equation of the tangent to the graph 3y3+x=x2+13y^3+x=x^2+1 at x=2x=2.
Implicit Differentiation
Find all the equations of the tangent lines to the curve y=x3+x2−xy=x^3+x^2-x that are parallel to the x-axis.
Find dydx\frac{dy}{dx} at x=0x=0 if xcos⁡(y2)=ycos⁡xx\cos\left(\frac{y}{2}\right)=y\cos x.
Implicit Differentiation: Tangent line
Find the equation of the tangent to the graph 3y3+x=x2+13y^3+x=x^2+1 at x=2x=2.
Implicit differentiation
Differentiate exy−tan⁡y=3x3+2xe^{xy}-\tan y=\frac{3}{x^3}+2x
Implicit Differentiation
Given x2+y=y2−4x^2+y=y^2-4, find y′y'.
Implicit Differentiation
Find dydx\displaystyle \frac{\text{d}y}{\text{d}x} for y3=2xy^3=2x.
Find the point(s) where x2−4x+6y+y2=−9 x^2-4x+6y+y^2 = −9 has horizontal and vertical tangent lines.
Find dydx\dfrac{dy}{dx} for the function ycos⁡x=x2+cos⁡yy\cos x=x^2+\cos y
Logarithmic for Implicitly Defined Function
Find dy/dxdy/dx at the point (1,1)(1,1) given xy=yxx^y=y^x
Practice: Tangent and Normal Lines with Implicit
Q:\textbf{Q:} Find the equation of the tangent and the normal lines to the curve x2cos⁡2y−sin⁡y=0x^2\cos^2y-\sin y=0 at the point (0,π)(0,\pi).
Implicit Second Derivative
Find d2ydx2\dfrac{d^2y}{dx^2} at the point (2,2)(2,2) given xy+y2=2xy+y^2=2
Implicit Differentiation
Evaluate the slope of the line tangent to the curve xy=x3y−6\sqrt{xy}=x^3y-6 at the point P(1,9)P(1,9).
Implicit with Trig
Find dy/dxdy/dx for xy=tan⁡(x+y2)\displaystyle xy=\tan(x+y^{2})
Implicit Differentiation
Let xx, yy satisfy the equation xy=6y−x+1x^y = 6y - x + 1. Find dydx\frac{dy}{dx} at the point (x,y)=(1,1/6)(x, y) = (1, 1/6).
Derivatives: Logarithmic Functions
Compute the derivative of f(x)=xx+1f(x) = x^{x + 1}. Remember that log⁡x=log⁡ex=ln⁡x\log x = \log_e x = \ln x.
Tangent lines: Implicit Differentiation
An equation of the tangent line to the curve x3+xln⁡y+y4=3x32+exx^3+x\ln y+y^4=3x^{\frac{3}{2}}+e^x at x=0x=0 is
Implicit Differentiation: Logarithmic Functions
For the following equations, solve for dydx\frac{dy}{dx} :
a) y=(5x2+3)sin⁡(x)y = (5x^2 + 3)^{\sin(x)}
b) x2y+3y2x2=x+yx^2y + 3y^2 x^2 = x + y
Evaluate the slope of the tangent line to the curve at the given point.
xy=x3y−6  at  P(1,9)\displaystyle \sqrt{xy}=x^3y-6\,\, at \,\,P(1,9)
Implicit differentiation
Find the derivative of the following:
yex+y2=x2ye^{x+y^2}=x^2
Implicit differentiation
Find the derivative of the following:
sin⁡(x+y)−sec⁡(x2+y2)=y\sin(x+y)-\mathrm{\sec}(x^2+y^2)=y
Implicit Differentiation
Evaluate the slope of the tangent line to the curve at the given point.
x3+y3=ysin⁡x+1,  at  P(0,1)x^3+y^3=y\sin{x}+1,\,\, \text{at}\,\,P(0,1)
Evaluate the slope of the tangent line to the curve at the given point.
xy=x3y−6  at  P(1,9)\displaystyle \sqrt{xy}=x^3y-6\,\, at \,\,P(1,9)
Evaluate the slope of the tangent line to the curve at the given point.
xy=x3y−6  at  P(1,9)\displaystyle \sqrt{xy}=x^3y-6\,\, at \,\,P(1,9)
Find the equation of the tangent line to the equation x3+ln⁡y=8x^3+\ln y=8 at the point (2, 1)
Evaluate the slope of the tangent line to the curve at the given point.
xy=x3y−6  at  P(1,9)\displaystyle \sqrt{xy}=x^3y-6\,\, at \,\,P(1,9)
Implicit Differentiation: Logarithmic Differentiation
Find the equation of the tangent line to
(sin⁡(xy))x=x1/4(\sin(xy))^x = x^{1/4}
at the point (12,π2)\left(\dfrac{1}{2},\dfrac{\pi}{2}\right).
Implicit Differentiation
Find the slope of the line tangent to the curve xy=x3y−6\sqrt{xy}=x^3y-6 at the point (1,9).
Implicit Differentiation
Find y'' if x3+y3=4.x^3+y^3=4.
Find dydx\frac{dy}{dx} given that exy−xy=2x2+1 e^{xy}-xy=2x^2+1
final114
Find y′y' for the function x4+x3y−xy2=1x^4+x^3y-xy^2=1
Differentiate the following functions.
(a) g(t)=(t5+t2)6tg(t)=(t^5+t^2)^{6t} (b) f(x)=x6xf(x)=\sqrt x^{6x} (c) f(x)=(x3+4)tan⁡xf(x)=(x^3+4)^{\tan x} (d) Finddydx\frac{dy}{dx} if ycos⁡(x)=xtan⁡(y)y\cos(x)=x\tan(y)
Differentiate y with respect to x in the equation 2x2+3xy−y2=12x^2+3xy-y^2=1.
Find dydx\frac{dy}{dx} given that exy−xy=2x2+1 e^{xy}-xy=2x^2+1
Evaluate the slope of the tangent line to the curve at the given point.
x3+y3=4xy,  at  P(2,2)x^3+y^3=4xy ,\,\, \text{at} \,\, P(2,2)
Evaluate the slope of the tangent line to the curve at the given point.
x3+y3=ysin⁡x+1,  at  P(0,1)x^3+y^3=y\sin{x}+1,\,\, \text{at}\,\,P(0,1)
Implicit Differentiation
Given x2+y=y2−4x^2+y=y^2-4, find y′y'.
Implicit Differentiation
Find dydx\displaystyle \frac{\text{d}y}{\text{d}x} for y3=2xy^3=2x.
Find the point(s) where x2−4x+6y+y2=−9 x^2-4x+6y+y^2 = −9 has horizontal and vertical tangent lines.
Find dydx\dfrac{dy}{dx} for the function ycos⁡x=x2+cos⁡yy\cos x=x^2+\cos y
Logarithmic for Implicitly Defined Function
Find dy/dxdy/dx at the point (1,1)(1,1) given xy=yxx^y=y^x
Implicit Second Derivative
Find d2ydx2\dfrac{d^2y}{dx^2} at the point (2,2)(2,2) given xy+y2=2xy+y^2=2
Practice: Tangent and Normal Lines with Implicit
Q:\textbf{Q:} Find the equation of the tangent and the normal lines to the curve x2cos⁡2y−sin⁡y=0x^2\cos^2y-\sin y=0 at the point (0,π)(0,\pi).
Implicit Differentiation
Evaluate the slope of the line tangent to the curve xy=x3y−6\sqrt{xy}=x^3y-6 at the point P(1,9)P(1,9).
Implicit with Trig
Find dy/dxdy/dx for xy=tan⁡(x+y2)\displaystyle xy=\tan(x+y^{2})
Find the slope of the tangent line to the curve ln⁡(x−y)+3y2=3\ln(x-y)+3y^2=3 at point (3,2)(3,2).
Find y′y' for the function x4+x3y−xy2=1x^4+x^3y-xy^2=1
Implicit Differentiation: Estimate of Implicit Function
Use a linear approximation to estimate the yy value of the curve described by x3+3xy+y3=5x^3+3xy+y^3=5 at the point for which x=0.1x=0.1 (leave it as an exact value if you're not allowed a calculator on the exam).
Find the point on the graph y2 = 4x + 5 where the tangent line is parallel to the line y = 2x + 184.
Concept Clarifier
Compute the second derivative of the implicit function y3=xcos⁡yy^3=x \cos y, where yy is a function of xx. Do not simplify.
Find the point(s) where x2−4x+6y+y2 = −9 has horizontal and vertical tangent lines.
Find the slope of the tangent line to the curve ln(x − y) + y2 = 4 at point (3,2).
(Express your answer as a fraction in lowest terms. If the answer is a negative number, put the negative sign in front of the entire fraction.)
Find the equation of the tangent line at the point (1,2)(1,2) of the curve y3−2x5y2=yln⁡(x)y^3-2x^5y^2=y\ln(x).
Find the derivative of sin⁡(x+y)−sec(x2+y2)=y\sin(x+y)-\mathrm{sec} (x^2+y^2)=y.
Find the derivative of y with respect to x of the following equation, y2+x5y3=5−ln⁡yy^2+x^5y^3=5-\ln y.
Given that x2+y=y2−4x^2+y=y^2-4, where y is dependent on x, find dydx\frac{dy}{dx}.
Implicit Differentiation
For the implicit equation x4+x3y−xy2=1x^4+x^3y-xy^2=1, where y = f(x), find y'.
Evaluate the slope of the tangent line to the curve at the given point.
xy=x3y−6  at  P(1,9)\displaystyle \sqrt{xy}=x^3y-6\,\, at \,\,P(1,9)
Find the tangent to the curve 4𝑦2 − 𝑒𝑥 + 𝑥 = 4𝑥 + 3 at the point where 𝑥 = 0 and 𝑦 is positive
Implicit Differentiation
Find all the equations of the tangent lines to the curve y=x3+x2−xy=x^3+x^2-x that are parallel to the x-axis.
Find dydx\frac{dy}{dx} at x=0x=0 if xcos⁡(y2)=ycos⁡xx\cos\left(\frac{y}{2}\right)=y\cos x.
Implicit Differentiation: Tangent line
Find the equation of the tangent to the graph 3y3+x=x2+13y^3+x=x^2+1 at x=2x=2.
Implicit differentiation
Differentiate exy−tan⁡y=3x3+2xe^{xy}-\tan y=\frac{3}{x^3}+2x
Implicit differentiation
Suppose 3x3+4y2=193x^3+4y^2=19, where x, yx,\ y are both functions of tt.
If dydt=3\frac{dy}{dt}=3, find dxdt\frac{dx}{dt} when y=2y=2.
Solve for dydx\frac{dy}{dx} :
x2y+3y2x2=x+yx^2y+3y^2x^2=x+y
Implicit Differentiation
Use implicit differentiation to calculate the derivative of
θ(x)=arctan⁡(x)\theta(x) = \arctan(x)
Implicit Differentiation
Find dydx\displaystyle \frac{\text{d}y}{\text{d}x} for ln⁡(x2+y2)+2xy=4\ln(x^2+y^2)+2xy=4.
Implicit Differentiation
Evaluate the slope of the tangent line to the curve at the given point.
x3y2+xtan⁡y=4 at P(x,y)\displaystyle x^3y^2+x\tan{y}=4 \, at\, P(x,y)
Evaluate the slope of the tangent line to the curve at the given point.
x2y3+xln⁡y+ysin⁡x=10  at  P(x,y)\displaystyle x^2y^3+x\ln{y}+y\sin{x}=10\,\, at \,\,P(x,y)
Practice: Implicit Differentiation
Find dydx\frac{dy}{dx} for the following
tan⁡yx=x\tan{\frac{y}{x}}=x