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If $y=f(g(x))$, then by the chain rule $\dfrac{dy}{dx}$ equals
A$\dfrac{df}{dx}\cdot\dfrac{dg}{dx}$
B$\dfrac{dy}{dg}\cdot\dfrac{dg}{dx}$
C$\dfrac{dy}{dx}+\dfrac{dg}{dx}$
D$\dfrac{df}{dg}$ only
Answer & Solution
Correct answer: B. $\dfrac{dy}{dg}\cdot\dfrac{dg}{dx}$
For a composite function $y=f(g(x))$, the chain rule gives $\dfrac{dy}{dx}=\dfrac{dy}{dg}\cdot\dfrac{dg}{dx}=f'(g(x))g'(x)$. Option A is not correctly written because $f$ is a function of $g(x)$, not directly of $x$ in that form.
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