Question

How do you find the derivative of `e^(2x)(x^2+5)`?

Answer 1

`f'(x)=2(x^2+x+5)e^{2x}`

Explanation:

Differentiating given function w.r.t. `x` as follows

`\frac{d}{dx}e^{2x}(x^2+5)`

`=e^{2x}\frac{d}{dx}(x^2+5)+(x^2+5)\frac{d}{dx}e^{2x}`

`=e^{2x}(2x)+(x^2+5)(2e^{2x})`

`=2(x^2+x+5)e^{2x}`