Question B.7: A useful formula that follows from Equation B.30 is the deri...
A useful formula that follows from Equation B. 30 is the derivative of the quotient of two functions. Show that
\frac{d}{d x} f(x)=\frac{d}{d x}[g(x) h(x)]=g \frac{d h}{d x}+h \frac{d g}{d x} (B.30)
\frac{d}{d x}\left[\frac{g(x)}{h(x)}\right]=\frac{h \frac{d g}{d x}-g \frac{d h}{d x}}{h^2}Write the quotient as g h^{-1} and use Equations B.29 and B.30:
\frac{d y}{d x}=n a x^{n-1} (B.29)
\begin{aligned}\frac{d}{d x}\left(\frac{g}{h}\right) & =\frac{d}{d x}\left(g h^{-1}\right)=g \frac{d}{d x}\left(h^{-1}\right)+h^{-1} \frac{d}{d x}(g) \\& =-g h^{-2} \frac{d h}{d x}+h^{-1} \frac{d g}{d x} \\& =\frac{h \frac{d g}{d x}-g \frac{d h}{d x}}{h^2}\end{aligned}Related Answered Questions
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