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Popular >

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

Solution

\frac{d}{d 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}

Popular Examples

y^2x^3dy-(x^3+1)dx=0

y^{2} x^{3} d y - (x^{3} + 1) d x = 0

-2(dy)/(dx)+6x^2=0

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(\partial)/(\partial x)(x^2y^4)

\frac{\partial}{\partial x} (x^{2} y^{4})

limit as x approaches 0 of (5x^2)/x

x \to 0 lim (\frac{5 x ^{2}}{x})

(\partial)/(\partial x)(x/(4x^2+9y^2))

\frac{\partial}{\partial x} (\frac{x}{4 x ^{2} + 9 y ^{2}})

Frequently Asked Questions (FAQ)

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