Question

Find the derivative of the function. m(t)=−2t(5t3−1)8 m′(t)=

Answer 1

`m'(t)=-2(5t^3-1)^8-240t^3(5t^3-1)^7`

Explanation:

Assuming you mean
`m(t)=-2t(5t^3-1)^8`

Let the following:

`f(t)=-2t\\f'(t)=-2\\g(t)=(5t^3-1)^8\\g'(t)=120t^2(5t^3-1)^7`

By product rule:

`m'(t)=f'(t)g(t)+f(t)g'(t)=-2(5t^3-1)^8-240t^3(5t^3-1)^7`