What is the derivative of i/x ?

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

What is the first derivative of i/x ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{d}{d x} (6 (sec (x) + tan (x))^{\frac{3}{2}})

\frac{\partial}{\partial x} (x^{5} sin (y))

\int x cos (7 x^{2}) d x

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

\int_{0}^{1} 3 + 9 x^{2} d x