Exercises for Question Type 1: Calculating second derivatives of functions - IB | RevisionDojo

Question Type 1: Calculating second derivatives of functions Exercises

Question 1

Find the second derivative $f''(x)$ for $f(x) = 3e^{2x}$ .

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Question 2

Find the second derivative $f''(x)$ for the function

f(x)=\frac{\cos(\ln x)\,e^{-x}}{x\ln x}

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Question 3

The objective of this question is to demonstrate the process of finding the second derivative of a polynomial function using the power rule.

Find the second derivative $f''(x)$ if $f(x)=x^4$ .

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Question 4

Find the second derivative $f''(x)$ for the function $f(x) = \ln(\sin x)$ .

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Question 5

Find the second derivative $f''(x)$ for the function $f(x) = \sin(\ln(x^2+1))$ .

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Question 6

Find the second derivative $f''(x)$ for $f(x) = \ln(x)$ .

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Question 7

Find the second derivative $f''(x)$ for $f(x) = \ln(x^2 + 1)$ .

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Question 8

Derivatives of inverse circular functions, including the chain rule and quotient rule.

Find the second derivative $f''(x)$ for $f(x) = \tan^{-1}(x^2)$ .

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Question 9

Find the second derivative $f''(x)$ for $f(x)=x^2e^x$ .

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Question 10

Find the second derivative $f''(x)$ for $f(x) = e^{-x} \cos x$ .

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Question 11

Find the second derivative $f''(x)$ for $f(x) = \sin(\ln x)$ .

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Question 12

Find the second derivative $f''(x)$ for $f(x) = \frac{\sin x}{x}$ .

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