What is the derivative of e/x ?

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

What is the first derivative of e/x ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

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

\int 3 x^{\frac{1}{5}} d x

y^{^{''}} + 100 y = 0

\int_{1}^{2} \frac{3}{t} d t

y = x^{2} - 3 x, (1, - 2)

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 cos (x)