Difference between revisions of "Quotient rule for derivatives"
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(Created page with "==Theorem== Let $f$ and $g$ be differentiable functions with $g'(x) \neq 0$ for all $x$. Then the following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} \left[ \dfrac{...") |
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Product rule for derivatives|next=Chain rule for derivatives}}: 3.3.4 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Product rule for derivatives|next=Chain rule for derivatives}}: $3.3.4$ |
Latest revision as of 17:22, 27 June 2016
Theorem
Let $f$ and $g$ be differentiable functions with $g'(x) \neq 0$ for all $x$. Then the following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} \left[ \dfrac{f(x)}{g(x)} \right] = \dfrac{g(x)f'(x)-f(x)g'(x)}{g(x)^2},$$ 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) ... (next): $3.3.4$
