What is the derivative of (e^x/(9x^2)) ?

The derivative of (e^x/(9x^2)) is (e^x(x-2))/(9x^3)

What is the first derivative of (e^x/(9x^2)) ?

The first derivative of (e^x/(9x^2)) is (e^x(x-2))/(9x^3)

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

\frac{e ^{x} ( x - 2 )}{9 x ^{3}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

= \frac{1}{9} \cdot \frac{\frac{d}{d x} ( e ^{x} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) e ^{x}}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{9} \cdot \frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{9} \cdot \frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}} : \frac{e ^{x} ( x - 2 )}{9 x ^{3}}

= \frac{e ^{x} ( x - 2 )}{9 x ^{3}}

x \to - 1 lim (\frac{x + 1}{x ^{2} + x})

n = 0 \sum \infty \frac{( - 1 ) ^{n + 1} ( x - 1 ) ^{n + 1}}{n + 1}

\frac{sin ( t )}{4 + 4 cos ( t )}

\int \frac{x ^{4}}{( 1 - x ^{2} ) ^{3}} d x

x^{2} ln (3 x)

What is the derivative of (e^x/(9x^2)) ?
The derivative of (e^x/(9x^2)) is (e^x(x-2))/(9x^3)
What is the first derivative of (e^x/(9x^2)) ?
The first derivative of (e^x/(9x^2)) is (e^x(x-2))/(9x^3)