Question

How do you find the derivative of `f(x)= (x^3)(e^(2x))`?

Answer 1

`dy/dx = x^2e^{2x}(3+2x)`

Explanation:

Product rule

`d/dx[uv] = {du}/dx v + {dv}/dx u`

`u=x^3`
`v=e^{2x}`

`dy/dx = d/dx[x^3]e^{2x}+d/dx[e^{2x}]x^3`

`dy/dx = 3x^2e^{2x}+2e^{2x}x^3`

`dy/dx = x^2e^{2x}(3+2x)`