Chain rule for derivatives

Theorem

Let $f$ and $g$ be differentiable functions for which we may define the composite function $f \circ g$. Then the following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} [(f\circ g)(x)] = f(g(x))g'(x),$$ where $\dfrac{\mathrm{d}}{\mathrm{d}x}$ denotes the derivative operator.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $3.3.5$