How do you differentiate $f (x) = e^{x} ((x^{3}) - 1)$ $f(x)= e^x((x^3)-1)$ using the product rule?

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Answer 1 · 2016-08-28T11:07:27

$e^{x} (x^{3} - 1) + 3 x^{2} e^{x}$ $e^x(x^3-1)+3x^2e^x$

$\frac{d}{d x} (e^{x} (x^{3} - 1))$ $frac{d}{dx}(e^x(x^3-1))$

applying product rule, $(fcdot g)^'=f^'cdot g+fcdot g^'$
$f=e^x,g=x^3-1$

$=frac{d}{dx}(e^x)(x^3-1)+frac{d}{dx}(x^3-1)e^x$

we know,
$frac{d}{dx}(e^x)=e^x$
and,
$frac{d}{dx}(x^3-1)=3x^2$

finally,
simplifying it,
$e^x(x^3-1)+3x^2e^x$

How do you differentiate f(x)= e^x((x^3)-1) f(x)=ex((x3)−1) f(x)= e^x((x^3)-1) using the product rule?