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Popular >

derivative of (x^3+2xe^x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

limit as x approaches 1000 of x^{4/3}

x \to 1000 lim (x^{\frac{4}{3}})

derivative of e^{x^x}derivative of

e^{x^{x}}

integral from-1 to 1 of (x^2-1/3)^2

\int_{- 1}^{1} (x^{2} - \frac{1}{3})^{2} d x

integral of (5x^2)/((3+x^3)^2)

\int \frac{5 x ^{2}}{( 3 + x ^{3} ) ^{2}} d x

integral of (sqrt(x^3)+1/(sqrt(x)))

\int (x^{3} + \frac{1}{x}) d x

Frequently Asked Questions (FAQ)

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