Question

a derivada de x^4.e^x

Answer 1

Regra do produto:

$\boxed{\boxed{\dfrac{d}{dx}f(x)\cdot g(x)=f'(x)\cdot g(x)+g'(x)\cdot f(x)}}$

Derivada de potências de x:

$\boxed{\boxed{\dfrac{d}{dx}x^{n}=n\cdot x^{n-1}}}$

Derivada de e^x:

$\boxed{\boxed{\dfrac{d}{dx}e^{x}=e^{x}}}$
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$f(x)=x^{4}\cdot e^{x}\\f'(x)=4\cdot x^{4-1}\cdot e^{x}+e^{x}\cdot x^{4}\\f'(x)=4x^{3}e^{x}+x^{4}e^{x}$

Colocando x³e^x em evidência:

$\boxed{\boxed{f'(x)=x^{3}e^{x}(4+x)}}$

Answer 2

$\sf \dfrac{d}{dx}[x^4e^x]=4x^3e^x+x^4e^x=x^3e^x[4+x]$