Chapter 5

Basic Differentiation

Educators


Problem 1

Find the derivative of each expression and simplify.
$\left(4 x^{2}+1\right)^{2}$

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Problem 2

Find the derivative of each expression and simplify.
$\left(x^{5}+3 x\right)^{2}$

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Problem 3

Find the derivative of each expression and simplify.
11$x^{7}$

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Problem 4

Find the derivative of each expression and simplify.
$18 x^{3}+12 x+11$

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Problem 5

Find the derivative of each expression and simplify.
$\frac{1}{2}\left(x^{12}+17\right)$

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Problem 6

Find the derivative of each expression and simplify.
$-\frac{1}{3}\left(x^{9}+2 x^{3}-9\right)$

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Problem 7

Find the derivative of each expression and simplify.
$\pi^{5}$

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Problem 8

Find the derivative of each expression and simplify.
$-8 x^{-8}+12 \sqrt{x}$

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Problem 9

Find the derivative of each expression and simplify.
$6 x^{-7}-4 \sqrt{x}$

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Problem 10

Find the derivative of each expression and simplify.
$x^{-5}+\frac{1}{x^{8}}$

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Problem 11

Find the derivative of each expression and simplify.
$\left(6 x^{2}+3\right)(12 x-4)$

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Problem 12

Find the derivative of each expression and simplify.
$\left(3-x-2 x^{3}\right)\left(6+x^{4}\right)$

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Problem 13

Find the derivative of each expression and simplify.
$e^{10}+\pi^{3}-7$

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Problem 14

Find the derivative of each expression and simplify.
$\left(\frac{1}{x}+\frac{1}{x^{2}}\right)\left(\frac{4}{x^{3}}-\frac{6}{x^{4}}\right)$

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Problem 15

Find the derivative of each expression and simplify.
$\sqrt{x}+\frac{1}{\sqrt{3}}$

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Problem 16

Find the derivative of each expression and simplify.
0

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Problem 17

Find the derivative of each expression and simplify.
$(x+1)^{3}$

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Problem 18

Find the derivative of each expression and simplify.
$\sqrt{x}+\sqrt[3]{x}+\sqrt[3]{x^{2}}$

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Problem 19

Find the derivative of each expression and simplify.
$x(2 x+7)(x-2)$

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Problem 20

Find the derivative of each expression and simplify.
$\sqrt{x}(\sqrt[3]{x}+\sqrt[5]{x})$

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