Implicit Differentiation

Find $\frac{dy}{dx}$ for the following

$\tan{\frac{y}{x}}=x$

Evaluate the slope of the tangent line to the curve at the given point.

Evaluate the slope of the tangent line to the curve at the given point.

Find $\displaystyle \frac{\text{d}y}{\text{d}x}$ for $\ln(x^2+y^2)+2xy=4$.

Use implicit differentiation to calculate the derivative of

Solve for $\frac{dy}{dx}$ :

For the following equations, solve for $\frac{dy}{dx}$ :

a) $y = (5x^2 + 3)^{\sin(x)}$

b) $x^2y + 3y^2 x^2 = x + y$

Suppose $3x^3+4y^2=19$, where $x,\ y$ are both functions of $t$.

If $\frac{dy}{dt}=3$, find $\frac{dx}{dt}$ when $y=2$.

Differentiate $e^{xy}-\tan y=\frac{3}{x^3}+2x$

Find the equation of the tangent to the graph $3y^3+x=x^2+1$ at $x=2$.

Find $\frac{dy}{dx}$ at $x=0$ if $x\cos\left(\frac{y}{2}\right)=y\cos x$.

Find all the equations of the tangent lines to the curve $y=x^3+x^2-x$ that are parallel to the x-axis.

Find the tangent to the curve 4��2 − ��𝑥 + 𝑥 = 4𝑥 + 3 at the point where 𝑥 = 0 and 𝑦 is positive

Evaluate the slope of the tangent line to the curve at the given point.

For the implicit equation $x^4+x^3y-xy^2=1$, where y = f(x), find y'.

Given that $x^2+y=y^2-4$, where y is dependent on x, find $\frac{dy}{dx}$.

Find the derivative of y with respect to x of the following equation, $y^2+x^5y^3=5-\ln y$.

Find the derivative of $\sin(x+y)-\mathrm{sec} (x^2+y^2)=y$.

Find the equation of the tangent line at the point $(1,2)$ of the curve $y^3-2x^5y^2=y\ln(x)$.

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 point(s) where x2−4x+6y+y2 = −9 has horizontal and vertical tangent lines.

Compute the second derivative of the implicit function $y^3=x \cos y$, where $y$ is a function of $x$. Do not simplify.

Find the point on the graph y2 = 4x + 5 where the tangent line is parallel to the line y = 2x + 184.

Use a linear approximation to estimate the $y$ value of the curve described by $x^3+3xy+y^3=5$ at the point for which $x=0.1$ (leave it as an exact value if you're not allowed a calculator on the exam).

Find $y'$ for the function $x^4+x^3y-xy^2=1$

Find the slope of the tangent line to the curve $\ln(x-y)+3y^2=3$ at point $(3,2)$.

Find $dy/dx$ for $\displaystyle xy=\tan(x+y^{2})$

Evaluate the slope of the line tangent to the curve $\sqrt{xy}=x^3y-6$ at the point $P(1,9)$.

$\textbf{Q:}$ Find the equation of the tangent and the normal lines to the curve $x^2\cos^2y-\sin y=0$ at the point $(0,\pi)$.

Find $\dfrac{d^2y}{dx^2}$ at the point $(2,2)$ given $xy+y^2=2$

Find $dy/dx$ at the point $(1,1)$ given $x^y=y^x$

Find $\dfrac{dy}{dx}$ for the function $y\cos x=x^2+\cos y$

Find the point(s) where $x^2-4x+6y+y^2 = −9$ has horizontal and vertical tangent lines.

Find $\displaystyle \frac{\text{d}y}{\text{d}x}$ for $y^3=2x$.

Given $x^2+y=y^2-4$, find $y'$.

Evaluate the slope of the tangent line to the curve at the given point.

$x^3+y^3=y\sin{x}+1,\,\, \text{at}\,\,P(0,1)$

Evaluate the slope of the tangent line to the curve at the given point.

$x^3+y^3=4xy ,\,\, \text{at} \,\, P(2,2)$

Find $\frac{dy}{dx}$ given that $e^{xy}-xy=2x^2+1$

Differentiate y with respect to x in the equation $2x^2+3xy-y^2=1$.

Differentiate the following functions.

(a) $g(t)=(t^5+t^2)^{6t}$ (b) $f(x)=\sqrt x^{6x}$ (c) $f(x)=(x^3+4)^{\tan x}$ (d) Find$\frac{dy}{dx}$ if $$$y\cos(x)=x\tan(y)$

Find $y'$ for the function $x^4+x^3y-xy^2=1$

Find $\frac{dy}{dx}$ given that $e^{xy}-xy=2x^2+1$

Find y'' if $x^3+y^3=4.$

Find the slope of the line tangent to the curve $\sqrt{xy}=x^3y-6$ at the point (1,9).

Find the equation of the tangent line to

at the point $\left(\dfrac{1}{2},\dfrac{\pi}{2}\right)$.

Evaluate the slope of the tangent line to the curve at the given point.

Find the equation of the tangent line to the equation $x^3+\ln y=8$ at the point (2, 1)

Evaluate the slope of the tangent line to the curve at the given point.

Evaluate the slope of the tangent line to the curve at the given point.

Evaluate the slope of the tangent line to the curve at the given point.

$x^3+y^3=y\sin{x}+1,\,\, \text{at}\,\,P(0,1)$

Find the derivative of the following:

Find the derivative of the following:

Evaluate the slope of the tangent line to the curve at the given point.

An equation of the tangent line to the curve $x^3+x\ln y+y^4=3x^{\frac{3}{2}}+e^x$ at $x=0$ is

Compute the derivative of $f(x) = x^{x + 1}$. Remember that $\log x = \log_e x = \ln x$.

Let $x$, $y$ satisfy the equation $x^y = 6y - x + 1$. Find $\frac{dy}{dx}$ at the point $(x, y) = (1, 1/6)$.

Find $dy/dx$ for $\displaystyle xy=\tan(x+y^{2})$

Evaluate the slope of the line tangent to the curve $\sqrt{xy}=x^3y-6$ at the point $P(1,9)$.

Find $\dfrac{d^2y}{dx^2}$ at the point $(2,2)$ given $xy+y^2=2$

$\textbf{Q:}$ Find the equation of the tangent and the normal lines to the curve $x^2\cos^2y-\sin y=0$ at the point $(0,\pi)$.

Find $dy/dx$ at the point $(1,1)$ given $x^y=y^x$

Find $\dfrac{dy}{dx}$ for the function $y\cos x=x^2+\cos y$

Find the point(s) where $x^2-4x+6y+y^2 = −9$ has horizontal and vertical tangent lines.

Find $\displaystyle \frac{\text{d}y}{\text{d}x}$ for $y^3=2x$.

Given $x^2+y=y^2-4$, find $y'$.

Differentiate $e^{xy}-\tan y=\frac{3}{x^3}+2x$

Find the equation of the tangent to the graph $3y^3+x=x^2+1$ at $x=2$.

Find $\frac{dy}{dx}$ at $x=0$ if $x\cos\left(\frac{y}{2}\right)=y\cos x$.

Find all the equations of the tangent lines to the curve $y=x^3+x^2-x$ that are parallel to the x-axis.

Find the equation of the tangent to the graph $3y^3+x=x^2+1$ at $x=2$.

For the implicit equation $x^4+x^3y-xy^2=1$, where y = f(x), find y'.

Evaluate the slope of the line tangent to the curve $\sqrt{xy}=x^3y-6$ at the point $P(1,9)$.

Find the equation of the tangent to the graph $3y^3+x=x^2+1$ at $x=2$.

Find the equation of the tangent to the graph $3y^3+x=x^2+1$ at $x=2$.

Evaluate the slope of the line tangent to the curve $\sqrt{xy}=x^3y-6$ at the point $P(1,9)$.

Find the tangent to the curve 4��2 − ��𝑥 + 𝑥 = 4𝑥 + 3 at the point where 𝑥 = 0 and 𝑦 is positive

An equation of the tangent line to the curve $x^3+x\ln y+y^4=3x^{\frac{3}{2}}+e^x$ at $x=0$ is

Find the derivative of the following:

Find the slope of the line tangent to the curve $\sqrt{xy}=x^3y-6$ at the point (1,9).

Find $\displaystyle \frac{\text{d}y}{\text{d}x}$ for $y^3=2x$.

Find y'' if $x^3+y^3=4.$

An equation of the tangent line to the curve $x^3+x\ln y+y^4=3x^{\frac{3}{2}}+e^x$ at $x=0$ is

Find the slope of the line tangent to the curve $\sqrt{xy}=x^3y-6$ at the point (1,9).

Differentiate $e^{xy}-\tan y=\frac{3}{x^3}+2x$

Find $\dfrac{d^2y}{dx^2}$ at the point $(2,2)$ given $xy+y^2=2$

Find the equation of the tangent line to

at the point $\left(\dfrac{1}{2},\dfrac{\pi}{2}\right)$.

An equation of the tangent line to the curve $x^3+x\ln y+y^4=3x^{\frac{3}{2}}+e^x$ at $x=0$ is

Find the equation of the tangent to the graph $3y^3+x=x^2+1$ at $x=2$.

Differentiate $e^{xy}-\tan y=\frac{3}{x^3}+2x$