Difference between revisions of "Chain rule for derivatives"
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Quotient rule for derivatives|next=}}: 3.3. | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Quotient rule for derivatives|next=}}: 3.3.5 |
Revision as of 08:09, 4 June 2016
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): 3.3.5
