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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{3} + 2, g = e^{x}

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

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

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

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

\int 9 x^{8} e^{5 x^{9}} d x

\frac{3}{x - 1}

y^{^{'}} - 2 y = - 3 y^{2}

\int arctan (t^{2}) d t

y = \frac{5}{x}

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