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Practice: Multiple Chain Rules
Related Topics
Wize University Calculus 2 Textbook > Review: Derivatives
Derivative Rule
9 Activities
Practice: Multiple Chain Rules
Find the derivative of
f
(
x
)
=
x
+
x
4
+
x
3
+
x
2
+
1
f\left(x\right)=x+\sqrt{x^4+\sqrt{x^3+\sqrt{x^2+1}}}
f
(
x
)
=
x
+
x
4
+
x
3
+
x
2
+
1
at
x
=
0
x=0
x
=
0
Enter the exact value of the derivative at
x
=
0
x=0
x
=
0
I don't know
Check Submission
More Derivative Rule Questions:
Practice: Derivative Rules (Level 2)
Find the rate of the change of the function
f
(
x
)
=
5
x
−
x
3
2
+
1
3
x
\displaystyle f(x)=\frac{5}{\sqrt{x}}-\frac{\sqrt[3]{x}}{2}+\frac{1}{3x}
f
(
x
)
=
x
5
−
2
3
x
+
3
x
1
at the point
x
=
1
x=1
x
=
1
.
Differentiation Rules
Find
d
d
x
(
sin
2
x
+
π
+
cos
2
x
+
5
7
)
\frac{d}{dx}(\sin^2{x}+\sqrt\pi+\cos^2{x}+5^7)
d
x
d
(
sin
2
x
+
π
+
cos
2
x
+
5
7
)
Differentiation Rules
Find
d
d
x
(
sin
2
x
+
π
+
cos
2
x
+
5
7
)
\frac{d}{dx}(\sin^2{x}+\sqrt\pi+\cos^2{x}+5^7)
d
x
d
(
sin
2
x
+
π
+
cos
2
x
+
5
7
)
Differentiation Rules
Find
d
d
x
(
sin
2
x
+
π
+
cos
2
x
+
5
7
)
\frac{d}{dx}(\sin^2{x}+\sqrt\pi+\cos^2{x}+5^7)
d
x
d
(
sin
2
x
+
π
+
cos
2
x
+
5
7
)
Differentiation Rules
Find
d
d
x
(
sin
2
x
+
π
+
cos
2
x
+
5
7
)
\frac{d}{dx}(\sin^2{x}+\sqrt\pi+\cos^2{x}+5^7)
d
x
d
(
sin
2
x
+
π
+
cos
2
x
+
5
7
)
Practice: Product Rule*
Suppose
g
(
x
)
g\left(x\right)
g
(
x
)
is differentiable,
f
(
x
)
=
x
2
g
(
x
)
f\left(x\right)=x^2g\left(x\right)
f
(
x
)
=
x
2
g
(
x
)
. Given that
f
′
(
3
)
=
30
f'\left(3\right)=30
f
′
(
3
)
=
30
,
f
′
′
(
3
)
=
19
f''\left(3\right)=19
f
′′
(
3
)
=
19
,
g
(
3
)
=
2
g\left(3\right)=2
g
(
3
)
=
2
, what is
g
′
(
3
)
g'\left(3\right)
g
′
(
3
)
and
g
′
′
(
3
)
g''\left(3\right)
g
′′
(
3
)
?
Practice: Quotient Rule
Find the derivative of
f
(
x
)
=
x
2
+
3
x
4
/
3
+
1
x
2
+
1
\displaystyle f(x)=\frac{x^2+3x^{4/3}+1}{x^2+1}
f
(
x
)
=
x
2
+
1
x
2
+
3
x
4/3
+
1
Practice: Derivative Rule (Level 3)
Practice: Derivative Rule
Given
f
(
t
)
=
2
t
3
(
t
+
1
t
)
t
\displaystyle f(t)=\frac{2t^3\left(t+\frac{1}{t}\right)}{\sqrt{t}}
f
(
t
)
=
t
2
t
3
(
t
+
t
1
)
, find
f
′
(
4
)
f'\left(4\right)
f
′
(
4
)
.
Differentiation Rules
Find
d
d
x
(
sin
2
x
+
π
+
cos
2
x
+
5
7
)
\frac{d}{dx}(\sin^2{x}+\sqrt\pi+\cos^2{x}+5^7)
d
x
d
(
sin
2
x
+
π
+
cos
2
x
+
5
7
)
Practice: Derivative Rules (Level 2)
Practice: Derivative Rules
Find the rate of the change of the function
f
(
x
)
=
5
x
−
x
3
2
+
1
3
x
\displaystyle f(x)=\frac{5}{\sqrt{x}}-\frac{\sqrt[3]{x}}{2}+\frac{1}{3x}
f
(
x
)
=
x
5
−
2
3
x
+
3
x
1
at the point
x
=
1
x=1
x
=
1
.