MathAnalysisCalculusDerivatives

A composite function and its derivative

Composite functions

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Which of the following statements is true regarding the derivative of a composite function $f(g(x))$ where $f$ and $g$ are both differentiable functions?

Select one option from the list

The derivative of

f(g(x))

is always equal to

f'(x)*g''(x)

The derivative of

f(g(x))

is always equal to

f'(g(x))*g'(x)

The derivative of

f(g(x))

is always equal to

f'(x)*g'(x)

The derivative of

f(g(x))

cannot be determined without knowing the specific functions

f

and

g

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