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)}

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

\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}}

\frac{d}{d x} (3 1 - 2 x)

\int \frac{7}{25 - x ^{2}} d x

2 x y

y^{^{'}} = y + sin (x) - cos (x)

f (x) = \frac{7 x - 5}{x ^{2} + 4 x}

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)}