Use the product rule to find the derivative?

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

1 Answer
Mar 8, 2018

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))