If $y=f(g(x))$, then by the chain rule $\dfrac{dy}{dx}$ equals

Question

Accepted 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.**

Answer

$\dfrac{df}{dx}\cdot\dfrac{dg}{dx}$

Answer

$\dfrac{dy}{dx}+\dfrac{dg}{dx}$

Answer

$\dfrac{df}{dg}$ only

If $y=f(g(x))$, then by the chain rule $\dfrac{dy}{dx}$ equals

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