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}\left[\frac{g(x)}{h(x)}\right]=\frac{h \frac{d g}{d x}-g \frac{d h}{d x}}{h^{2}}
\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]
We can write the quotient as g h^{-1} and then apply Equations B.29 and B.30:
\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{d \frac{d g}{d x}-g \frac{d h}{d x}}{h^{2}}\end{aligned}
\frac{d y}{d x}=n a x^{n-1} [B.29]
Related Answered Questions
Question: B.6
Verified Answer:
We can rewrite this function as y(x)= x^{3...
Question: B.5
Verified Answer:
By applying Equation B.29 to each term independent...
Question: B.2
Verified Answer:
From (2), x = y + 2. Substitution of this equation...