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Popular >

derivative of (x^3+9e^x)

Solution

\frac{d}{d x} ((x^{3} + 9) e^{x})

Solution

3 x^{2} e^{x} + e^{x} (x^{3} + 9)

Solution steps

\frac{d}{d x} ((x^{3} + 9) e^{x})

Apply the Product Rule:

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

f = x^{3} + 9, g = e^{x}

= \frac{d}{d x} (x^{3} + 9) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 9)

\frac{d}{d x} (x^{3} + 9) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 9)

Popular Examples

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\int_{2}^{7} \frac{4}{8 x - 11} d x

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\int_{\frac{1}{7}}^{3} 14 x ln (7 x) d x

(\partial)/(\partial x)((5y)/(x^2+1))

\frac{\partial}{\partial x} (\frac{5 y}{x ^{2} + 1})

Frequently Asked Questions (FAQ)

What is the derivative of (x^3+9e^x) ?
The derivative of (x^3+9e^x) is 3x^2e^x+e^x(x^3+9)
What is the first derivative of (x^3+9e^x) ?
The first derivative of (x^3+9e^x) is 3x^2e^x+e^x(x^3+9)