Assume the functions are differentiable on suitable open intervals, with the composite argument in t

Question

Assume the functions are differentiable on suitable open intervals, with the composite argument in the domain of the outer function. For the quotient, work where $g(x)\ne0$.

Let ${\mathrm{h}(x) = \frac{\mathrm{f}(x)}{\mathrm{g}(x)}}$. Show that ${\mathrm{h}'(x) = \frac{\mathrm{f}'(x)\mathrm{g}(x) - \mathrm{f}(x)\mathrm{g}'(x)}{[\mathrm{g}(x)]^{2}}}$.

Accepted Answer

$\mathrm{h}'(x)=\dfrac{\mathrm{f}'(x)\mathrm{g}(x)-\mathrm{f}(x)\mathrm{g}'(x)}{[\mathrm{g}(x)]^2}$, where $\mathrm{g}(x)\ne0$ (shown).

Proof of the Quotient Rule of Differentiation

Proof of the Quotient Rule of Differentiation

Solution:

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