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Popular >

derivative of x/(e^{2x})

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

= \frac{1 \cdot e ^{2 x} - e ^{2 x} \cdot 2 x}{( e ^{2 x} ) ^{2}}

Simplify

\frac{1 \cdot e ^{2 x} - e ^{2 x} \cdot 2 x}{( e ^{2 x} ) ^{2}} : \frac{1 - 2 x}{e ^{2 x}}

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

Graph

Popular Examples

y^{^{'}} + 8 x^{2} y = x^{2}

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\int \frac{cos ( t )}{5 + sin ( t )} d t

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Frequently Asked Questions (FAQ)

What is the derivative of x/(e^{2x}) ?
The derivative of x/(e^{2x}) is (1-2x)/(e^{2x)}
What is the first derivative of x/(e^{2x}) ?
The first derivative of x/(e^{2x}) is (1-2x)/(e^{2x)}