Question

Use the product rule to find the derivative?

`f(x)= (6sqrt((x))-2)(5sqrt(x)+7)`

Answer 1

`d/dx(g(x) *h(x)) = g'(x)*h(x)+ h'(x)*g(x)`

Explanation:

Here ,
`g(x) = (6√x−2)`
`h(x) = (5√x+7)`

`g'(x) = 3/sqrt(x)`
`h'(x) = 5/(2*sqrt(x))`

by product rule:

`d/dxf(x) =(6√x−2)*5/(2*sqrt(x)) + (5√x+7)* 3/sqrt(x)`

`=> (3 (5 sqrt(x) + 7))/sqrt(x) + (5 (6 sqrt(x) - 2))/(2 sqrt(x))`