Question

Yea thank goodness is not the only part I know

Answer 1

`y=√(-5e^x+12x)`

a.

Insides:

`u=-5e^x+12x`

Outside:

`y=√(u)`

b.

Use the chain rule to find the derivate:

`(d)/(dx)(y(u))=(d)/(du)(y(u))*(d)/(dx)u`
`\begin{gathered} (d)/(dx)(y)=(d)/(du)√(u)*(d)/(dx)(-5e^x+12x) \\ \\ (dy)/(dx)=(1)/(2√(u))*(-5e^x+12) \\ \\ (dy)/(dx)=(-5e^x+12)/(2√(u)) \\ \\ (dy)/(dx)=(-5e^x+12)/(2√(-5e^x+12x)) \\ \end{gathered}`

Derivate:

`(dy)/(dx)=(-5e^x+12)/(2√(-5e^x+12x))`