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=((1)/(2))x^8 \end{gathered}`

so:

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

Power rule