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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

Popular Examples

sum from n=0 to infinity of 5/(n!)

n = 0 \sum \infty \frac{5}{n !}

derivative of 1/(x^2+9)

\frac{d}{d x} (\frac{1}{x ^{2} + 9})

slope of (3,-6),(5,-5)slope

(3, - 6), (5, - 5)

area y=x^3-1,y=x-1 area

y = x^{3} - 1, y = x - 1

sum from n=0 to infinity of (3^n)/(5^{2n+1)}

n = 0 \sum \infty \frac{3 ^{n}}{5 ^{2 n + 1}}

Frequently Asked Questions (FAQ)

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