Chain rule for derivatives
From specialfunctionswiki
Revision as of 03:16, 4 June 2016 by Tom (talk | contribs) (Created page with "==Theorem== Let $f$ and $g$ be differentiable functions for which we may define the composite function $f \circ g$. Then the following formula holds: $$\dfrac{\mathrm{d}}{...")
Theorem
Let $f$ and $g$ be differentiable functions for which we may define the composite function $f \circ g$. Then the following formula holds: $$\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.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): 3.3.4
