UPCET / UPSEE Chain Rule — practice questions

Explore 2 free Chain Rule questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Chain Rule questions and exercises with answers

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The **chain rule** states $\dfrac{dy}{dx}$ for $y = f(g(x))$ is:Read the answer and worked solution →If $y = \sin(\cos x)$, then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →

Worked practice questions

The chain rule states $\dfrac{dy}{dx}$ for $y = f(g(x))$ is:

$f'(g(x)) + g'(x)$
$f'(g(x)) \cdot g'(x)$
$f'(x) \cdot g'(x)$
$f'(g(x))$

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Correct answer: B. $f'(g(x)) \cdot g'(x)$

**Chain rule:** $dy/dx = f'(g(x)) \cdot g'(x)$. Differentiate outer function evaluated at inner, then multiply by derivative of inner.

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If $y = \sin(\cos x)$, then $\dfrac{dy}{dx}$ equals:

$-\cos(\cos x) \cdot \sin(\cos x)$
$-\sin x \cos(\cos x)$
$\sin x \cdot \cos(\cos x)$
$\cos(\cos x)$

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Correct answer: B. $-\sin x \cos(\cos x)$

Chain rule: $dy/dx = \cos(\cos x) \cdot d/dx(\cos x) = \cos(\cos x) \cdot (-\sin x) = -\sin x \cos(\cos x)$.