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Popular Calculus >

derivative of (e^x/(x^n))

Solution

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

Solution

\frac{e ^{x} ( x - n )}{x ^{1 + n}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{n}) = n x^{n - 1}

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

Simplify

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

= \frac{e ^{x} ( x - n )}{x ^{1 + n}}

Graph

Popular Examples

t(dx)/(dt)=x-2t

t \frac{d x}{d t} = x - 2 t

sum from n=1 to infinity of 2+n/(3n+2)

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

inverse oflaplace (s^2)/((s+5)(s^2+2^2))

in v erse l a pl a ce \frac{s ^{2}}{( s + 5 ) ( s ^{2} + 2 ^{2} )}

integral of sin(2x-pi/4)

\int sin (2 x - \frac{π}{4}) d x

limit as x approaches 1 of 1

x \to 1 lim (1)

Frequently Asked Questions (FAQ)

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