Question

Use the General Power Rule to find the derivative of the function.y = (5x3 +2)2y' =

Answer 1

`y=(5x^3+2)\placeholder{⬚}^2`

General power rule:

`(d)/(dx)u^n=nu^(n-1)`

1. Use the change rule as follow:

`\begin{gathered} u=5x^3+2 \\ \\ y^(\prime)=(d)/(du)u^2*(d)/(dx)(5x^3+2) \\ \\ y^(\prime)=(d)/(du)u^2*((d)/(dx)5x^3+(d)/(dx)2) \end{gathered}`

2. Use the general power rule:

`\begin{gathered} y^(\prime)=2u(15x^2+0) \\ \\ y^(\prime)=2u(15x^2) \end{gathered}`

3. Substitute u by its value and simplify:

`\begin{gathered} y^(\prime)=2(5x^3+2)(15x^2) \\ y^(\prime)=30x^2(5x^3+2) \\ y^(\prime)=150x^5+60x^2 \end{gathered}`

Then, the derivate of the given function is:

`y^(\prime)=150x^5+60x^2`