What is the derivative of e(1/x) ?

The derivative of e(1/x) is -e/(x^2)

What is the first derivative of e(1/x) ?

The first derivative of e(1/x) is -e/(x^2)

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

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

Solution steps

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

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

16 x y^{^{'}} - 2 y = - \frac{x ^{2}}{y ^{15}}

tan (2 x)

\int (\frac{( 1 + 4 ln ( x ) ) ^{5}}{x}) d x

\int \frac{e ^{4 x} + 3}{e ^{3 x}} d x

What is the derivative of e(1/x) ?
The derivative of e(1/x) is -e/(x^2)
What is the first derivative of e(1/x) ?
The first derivative of e(1/x) is -e/(x^2)