What is the derivative of e^xx^3 ?

The derivative of e^xx^3 is e^xx^3+3x^2e^x

What is the first derivative of e^xx^3 ?

The first derivative of e^xx^3 is e^xx^3+3x^2e^x

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\frac{d}{d x} (e^{x} x^{3})

e^{x} x^{3} + 3 x^{2} e^{x}

Solution steps

\frac{d}{d x} (e^{x} x^{3})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = x^{3}

= \frac{d}{d x} (e^{x}) x^{3} + \frac{d}{d x} (x^{3}) e^{x}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

\frac{d y}{d x} = (\frac{( 2 y + 7 )}{( 8 x + 9 )})^{2}

\frac{s ( s + 2 )}{( s + 1 ) ^{2}}

\int \frac{1}{e ^{y} sin ^{2} ( e ^{- y} )} d y

f (x) = \frac{1}{x ^{7} + 2}

\int (x^{6}) d x

What is the derivative of e^xx^3 ?
The derivative of e^xx^3 is e^xx^3+3x^2e^x
What is the first derivative of e^xx^3 ?
The first derivative of e^xx^3 is e^xx^3+3x^2e^x