What is the derivative of 3x^2e^x+e^x(x^3+4) ?

The derivative of 3x^2e^x+e^x(x^3+4) is e^xx^3+6e^xx^2+6e^xx+4e^x

What is the first derivative of 3x^2e^x+e^x(x^3+4) ?

The first derivative of 3x^2e^x+e^x(x^3+4) is e^xx^3+6e^xx^2+6e^xx+4e^x

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derivative of

3 x^{2} e^{x} + e^{x} (x^{3} + 4)

e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 4 e^{x}

Solution steps

\frac{d}{d x} (3 x^{2} e^{x} + e^{x} (x^{3} + 4))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 x^{2} e^{x}) + \frac{d}{d x} (e^{x} (x^{3} + 4))

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

\frac{d}{d x} (e^{x} (x^{3} + 4)) = e^{x} (x^{3} + 4) + 3 x^{2} e^{x}

= 3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 4) + 3 x^{2} e^{x}

Simplify

3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 4) + 3 x^{2} e^{x} : e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 4 e^{x}

= e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 4 e^{x}

\int x^{5} e^{x^{6}} d x

(- 3.5) (2.1)

\int_{0}^{2} \frac{x}{2} d x

\int \frac{1}{1 - t ^{2}} d t

\frac{\partial}{\partial x} (e^{- 2 x} sin (2 x))

What is the derivative of 3x^2e^x+e^x(x^3+4) ?
The derivative of 3x^2e^x+e^x(x^3+4) is e^xx^3+6e^xx^2+6e^xx+4e^x
What is the first derivative of 3x^2e^x+e^x(x^3+4) ?
The first derivative of 3x^2e^x+e^x(x^3+4) is e^xx^3+6e^xx^2+6e^xx+4e^x