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Popular >

derivative of f(x)=(x)^3e^{(3x)}

Solution

derivative of

f (x) = (x)^{3} e^{(3 x)}

Solution

3 x^{2} e^{3 x} + e^{3 x} \cdot 3 x^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 3 x^{2} e^{3 x} + e^{3 x} \cdot 3 x^{3}

Graph

Popular Examples

derivative of 1/(sqrt(8+x^2))

\frac{d}{d x} (\frac{1}{8 + x ^{2}})

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\int 4 x^{2} + 1 d x

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f (x) = 6 x + 5

(\partial)/(\partial x)(((4x-4y))/(4x+3y))

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x)^3e^{(3x)} ?
The derivative of f(x)=(x)^3e^{(3x)} is 3x^2e^{3x}+e^{3x}*3x^3
What is the first derivative of f(x)=(x)^3e^{(3x)} ?
The first derivative of f(x)=(x)^3e^{(3x)} is 3x^2e^{3x}+e^{3x}*3x^3