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Popular >

derivative of f(x)=sqrt(x)e^{2x}

Solution

derivative of

f (x) = x e^{2 x}

Solution

\frac{e ^{2 x}}{2 x} + 2 e^{2 x} x

Solution steps

\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}

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} e^{2 x} + e^{2 x} \cdot 2 x

\frac{1}{2 x} e^{2 x} = \frac{e ^{2 x}}{2 x}

= \frac{e ^{2 x}}{2 x} + 2 e^{2 x} x

Popular Examples

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\int (2 x - 1) sin (4 x y) d x

derivative of 2/(t^4)derivative of

\frac{2}{t ^{4}}

sum from n=1 to infinity of ((1))/(2n+7)

n = 1 \sum \infty \frac{( 1 )}{2 n + 7}

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n = 2 \sum \infty 1 - \frac{1}{n ^{2}}

derivative of y=x^4ln(x)derivative of

y = x^{4} ln (x)

Frequently Asked Questions (FAQ)

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