Exercises for Question Type 1: Finding the derivatives of more complex functions that involve trigonometric, exponential functions - IB | RevisionDojo

Question Type 1: Finding the derivatives of more complex functions that involve trigonometric, exponential functions Exercises

Question 1

Differentiate $p(x)=3\tan x - x^{-5} + 6\ln x$ .

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Question 2

Differentiate $h(x)=2x^{-1}+4x^{\frac{3}{2}}+\ln x$ .

[3]

Question 3

Differentiate $q(x)=x^{\frac{2}{3}}+4\csc x+2e^x$ .

[3]

Question 4

Differentiate $r(x)=7\ln x-9\sec x+x^{-\frac13}$ .

[3]

Question 5

Differentiate $t(x)=-8\ln x+2\cot x-5x^{-2}$ .

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Question 6

Differentiate $u(x)=x^{5}+2x^{-1}+3e^x-4\cos x+\ln x$ .

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Question 7

Differentiate the given function with respect to $x$ .

Differentiate $v(x)=x^{\frac{1}{3}}-3\tan x+7\ln x-e^x$ .

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Question 8

Given a function $f(x)$ , find the value of its derivative at a specific point.

Given $f(x)=2\ln x+3e^x-4\sin x+x^{-\frac{1}{2}}$ , find the exact value of $f'(1)$ .

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Question 9

Find $g'(x)$ for $g(x) = 5e^x - 7\cos x + x^{\frac{1}{2}}$ . [3 marks]

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Question 10

Differentiate $s(x)=4e^x+5\sin x+3x^{\frac{7}{4}}$ . [3 marks]

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Question 11

Differentiate $w(x)=\frac{1}{x^2}+4\ln x+6\sin x$ .

[3]

Question 12

Differentiate $f(x) = \frac{4}{9}x^{-3} + 3\ln x - \sin x$ with respect to $x$ .

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