Question B.6: Find the derivative of y(x) = x³/(x + 1)² with respect to x.
Find the derivative of y(x) = x³/(x + 1)² with respect to x.
Rewrite the function as a product:
y(x)=x^3(x+1)^{-2}Use Equation B.30 to find the derivative:
\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)
\begin{aligned}\frac{d y}{d x} & =(x+1)^{-2} \frac{d}{d x}\left(x^3\right)+x^3 \frac{d}{d x}(x+1)^{-2} \\& =(x+1)^{-2} 3 x^2+x^3(-2)(x+1)^{-3} \\\frac{d y}{d x} & =\frac{3 x^2}{(x+1)^2}-\frac{2 x^3}{(x+1)^3}=\frac{x^2(x+3)}{(x+1)^3}\end{aligned}Related Answered Questions
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