Question

How do you differentiate `y=(-7x^4+10x^(2/5)+8)(x^2+10)` using the product rule?

Answer 1

`(dy)/(dx)=(-7x^4+10x^(2/5)+8)2x+(x^2+10)(-28x^3+4x^(-3/5))`

Explanation:

Solve by using the product rule.
`(dy)/(dx)=f(x)g'(x)+g(x)f'(x)`

`f(x)=-7x^4+10x^(2/5)+8`
`g(x)=x^2+10`
`f'(x)=28x^3+4x^(-3/5)`
`g'(x)=2x`

`(dy)/(dx)=(-7x^4+10x^(2/5)+8)2x+(x^2+10)(-28x^3+4x^(-3/5))`