What is the derivative of (e^x)/(x^9) ?

The derivative of (e^x)/(x^9) is (e^x(x-9))/(x^{10)}

What is the first derivative of (e^x)/(x^9) ?

The first derivative of (e^x)/(x^9) is (e^x(x-9))/(x^{10)}

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derivative of

\frac{e ^{x}}{x ^{9}}

\frac{e ^{x} ( x - 9 )}{x ^{10}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{x ^{9}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) x ^{9} - \frac{d}{d x} ( x ^{9} ) e ^{x}}{( x ^{9} ) ^{2}}

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

\frac{d}{d x} (x^{9}) = 9 x^{8}

= \frac{e ^{x} x ^{9} - 9 x ^{8} e ^{x}}{( x ^{9} ) ^{2}}

Simplify

\frac{e ^{x} x ^{9} - 9 x ^{8} e ^{x}}{( x ^{9} ) ^{2}} : \frac{e ^{x} ( x - 9 )}{x ^{10}}

= \frac{e ^{x} ( x - 9 )}{x ^{10}}

2 x + 3 x^{2} + 4

y = (x^{2} + 1) sin (x)

2 cos^{2} (x) - 1

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

(1 + 2 x)^{x}

What is the derivative of (e^x)/(x^9) ?
The derivative of (e^x)/(x^9) is (e^x(x-9))/(x^{10)}
What is the first derivative of (e^x)/(x^9) ?
The first derivative of (e^x)/(x^9) is (e^x(x-9))/(x^{10)}