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

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

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

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

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

\frac{e ^{x} x - e ^{x}}{9 x ^{2}}

Solution steps

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

Take the constant out:

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

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

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 - \frac{d x}{d x} e ^{x}}{x ^{2}}

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

\frac{d x}{d x} = 1

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

Simplify

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

= \frac{e ^{x} x - e ^{x}}{9 x ^{2}}

\int_{0}^{1} (2 x - 3) (5 x + 1) d x

\int \frac{1}{2} sin (x) d x

x \to 8 + lim (lo g_{5} (x - 8))

\int_{0}^{2} \frac{x}{x + 1} d x

\frac{d}{d x} (lo g_{5} (\frac{6 x ^{3} + 4}{2 x ^{3} - 3}))

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