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Popular >

derivative of y=x^3e^{4x}

Solution

derivative of

y = x^{3} e^{4 x}

Solution

3 x^{2} e^{4 x} + e^{4 x} \cdot 4 x^{3}

Solution steps

\frac{d}{d x} (x^{3} e^{4 x})

Apply the Product Rule:

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

f = x^{3}, g = e^{4 x}

= \frac{d}{d x} (x^{3}) e^{4 x} + \frac{d}{d x} (e^{4 x}) x^{3}

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

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= 3 x^{2} e^{4 x} + e^{4 x} \cdot 4 x^{3}

Graph

Popular Examples

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\int \frac{e ^{- 2 x} + e ^{2 x}}{2} d x

tangent of f(x)=(18)/((2x+4)^2),\at x=9 tangent of

f (x) = \frac{18}{( 2 x + 4 ) ^{2}}, at x = 9

integral of cos(2x)e^{2x}

\int cos (2 x) e^{2 x} d x

(\partial)/(\partial x)(5^{xy})

\frac{\partial}{\partial x} (5^{x y})

limit as x approaches 0 of x^2sin(3/x)

x \to 0 lim (x^{2} sin (\frac{3}{x}))

Frequently Asked Questions (FAQ)

What is the derivative of y=x^3e^{4x} ?
The derivative of y=x^3e^{4x} is 3x^2e^{4x}+e^{4x}*4x^3
What is the first derivative of y=x^3e^{4x} ?
The first derivative of y=x^3e^{4x} is 3x^2e^{4x}+e^{4x}*4x^3