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Popular >

derivative of 8xe^{2x}

Solution

\frac{d}{d x} (8 x e^{2 x})

Solution

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

Solution steps

\frac{d}{d x} (8 x e^{2 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (x e^{2 x})

Apply the Product Rule:

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

f = x, g = e^{2 x}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

= 8 (1 \cdot e^{2 x} + e^{2 x} \cdot 2 x)

Simplify

= 8 (e^{2 x} + 2 e^{2 x} x)

Popular Examples

integral of (e^x)/((8-e^x)^2)

\int \frac{e ^{x}}{( 8 - e ^{x} ) ^{2}} d x

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\int \frac{1 - cos ( 2 x ^{2} )}{x ^{2}} d x

derivative of y=tan^3(x)derivative of

y = tan^{3} (x)

derivative of (-x/(sqrt(16-x^2)))

\frac{d}{d x} (\frac{- x}{16 - x ^{2}})

inverse oflaplace 1/(s^2+4s+4)inverse laplace

\frac{1}{s ^{2} + 4 s + 4}

Frequently Asked Questions (FAQ)

What is the derivative of 8xe^{2x} ?
The derivative of 8xe^{2x} is 8(e^{2x}+2e^{2x}x)
What is the first derivative of 8xe^{2x} ?
The first derivative of 8xe^{2x} is 8(e^{2x}+2e^{2x}x)