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Popular >

derivative of (x^3+3e^x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

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\int_{0}^{5} \frac{1}{x ^{\frac{5}{2}}} d x

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Frequently Asked Questions (FAQ)

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