Question

How do you differentiate `f(x)=(x^2+4x)*(x^3+2x+1)` using the product rule?

Answer 1

Product rule states that for `y=f(x)g(x)`, then `(dy)/(dx)=f'(x)g(x)+f(x)g'(x)`.

Explanation:

`(dy)/(dx)=(2x+4)(x^3+2x+1)+(x^2+4x)(3x^2+2)`

`(dy)/(dx)=(2x^4+4x^3+4x^2+10x+4)+(3x^4+12x^3+2x^2+8x)`

`(dy)/(dx)=5x^4+16x^3+6x^2+18x+4`