Question

How do you differentiate `f(x) =x^3sqrt(2x+1)` using the product rule?

Answer 1

`(df)/(dx)=3x^2sqrt(2x+1)+x^3/sqrt(2x+1)`

Explanation:

According to product rule, if `f(x)=g(x)xxh(x)`

then `(df)/(dx)=(dg)/(dx)xxh(x)+(dh)/(dx)xxg(x)`

Hence, as `f(x)=x^3sqrt(2x+1)`

then `(df)/(dx)=3x^2xxsqrt(2x+1)+1/2(2x+1)^(-1/2)xx2xx x^3`

i.e. `(df)/(dx)=3x^2sqrt(2x+1)+x^3/sqrt(2x+1)`