What is the derivative of (e^x/(x^5)) ?

The derivative of (e^x/(x^5)) is (e^x(x-5))/(x^6)

What is the first derivative of (e^x/(x^5)) ?

The first derivative of (e^x/(x^5)) is (e^x(x-5))/(x^6)

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\frac{d}{d x} (\frac{e ^{x}}{x ^{5}})

\frac{e ^{x} ( x - 5 )}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{x ^{5}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) x ^{5} - \frac{d}{d x} ( x ^{5} ) e ^{x}}{( x ^{5} ) ^{2}}

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{e ^{x} x ^{5} - 5 x ^{4} e ^{x}}{( x ^{5} ) ^{2}}

Simplify

\frac{e ^{x} x ^{5} - 5 x ^{4} e ^{x}}{( x ^{5} ) ^{2}} : \frac{e ^{x} ( x - 5 )}{x ^{6}}

= \frac{e ^{x} ( x - 5 )}{x ^{6}}

\frac{d}{d x} ((1 - \frac{x}{7})^{- 7})

\frac{d}{d r} (\frac{1}{r})

\frac{d}{d x} (9 arctan (x))

f (x) = \frac{x ^{2} + 3 x - 2}{x}

What is the derivative of (e^x/(x^5)) ?
The derivative of (e^x/(x^5)) is (e^x(x-5))/(x^6)
What is the first derivative of (e^x/(x^5)) ?
The first derivative of (e^x/(x^5)) is (e^x(x-5))/(x^6)