Question

Find the derivative of the function: $f\left(x\right)=x^2{e}^{3x}\forall x\in R$

Answer 1

Consider the given equation,

$f\left(x\right)=x^2{e}^{3x}\forall x\in R$

Now, $f\left(x\right)=x^2{e}^{3x}$

Differentiate both sides we get

$f^{{}^{\prime }}\left(x\right)=x^2\frac{d}{dx}{e}^{3x}+e^{3x}\frac{d}{dx}{x}^2$

$=x^2.3x.e^{3x}+e^{3x}.2x$

$=3x^3.e^{3x}+2x.e^{3x}$

$=x.e^{3x}.(3x^2+2)$

Hence, this is the answer.