Question

Given y = f(u) and u = g(x), find = f’(g(x))g’(x).y = 8u+ 3, U=(1/2)x^8Dy/dx=

Answer 1

$\begin{gathered} y=f(u)=8u+3 \\ u=(\frac{1}{2})x^8 \end{gathered}$

so:

$\begin{gathered} y=8(\frac{1}{2}x^8)+3 \\ y=4x^8+3 \end{gathered}$$\begin{gathered} \frac{dy}{dx}=4(8x^{8-1})+0 \\ \frac{dy}{dx}=12x^7 \end{gathered}$

Power rule