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Exercises for Question Type 2: Applying chain rule on composite functions - IB | RevisionDojo

Question 1

Calculus: Chain Rule

Find the derivative of

$f(x) = \sin^3(2x+1).$

[3]

Question 2

Candidates should be able to differentiate composite functions using the chain rule.

Compute the derivative of $f(x) = \ln(\sin x).$

[2]

Question 3

Calculus: Differentiation using the chain rule.

Differentiate the function $f(x)=\ln\bigl(e^x+1\bigr).$

[2]

Question 4

The student is required to find the derivative of a composite function involving the inverse tangent function, specifically $f(x) = \arctan(3x^2+1)$ , using the chain rule.

Find the derivative of $f(x) = \arctan(3x^2 + 1)$ .

[4]

Question 5

Differentiate the function $f(x) = \sin(\ln x)$ where $x > 0$ .

[2]

Question 6

Find $f'(x)$ if $f(x)=e^{\sin(x^2)}.$

[4]

Question 7

Find the derivative of the function $f(x) = \ln(x^2 + 1) + \sin(e^{3x})$

[4]

Question 8

Find $f'(x)$ for $f(x) = \sqrt{1 + e^{3x}}.$

[3]

Question 9

Differentiation using the chain rule.

Find the derivative of $f(x) = \left(\ln(x+1)\right)^3$ .

[3]

Question 10

This question requires the application of the chain rule to differentiate a composite function involving an exponential function and a power.

Differentiate the function $f(x)=\bigl(e^{x^2}+1\bigr)^4.$

[3]

Question 11

Compute $f'(x)$ if $f(x) = \left(\cos(x^2)\right)^5.$

[3]

Question 12

The question requires the application of the chain rule to a composite function involving natural logarithms, trigonometric functions, and exponential functions.

Differentiate the function $f(x) = \ln(\sin(e^x))$ .

[3]

Question Type 2: Applying chain rule on composite functions Exercises