Find the Derivative – d/dx c/x

$\frac{c}{x}$

Since $c$ is constant with respect to $x$ , the derivative of $\frac{c}{x}$ with respect to $x$ is $c \frac{d}{d x} [\frac{1}{x}]$ .

$c \frac{d}{d x} [\frac{1}{x}]$

Rewrite $\frac{1}{x}$ as $x^{- 1}$ .

$c \frac{d}{d x} [x^{- 1}]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = - 1$ .

$c (- x^{- 2})$

Simplify the expression.

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Move $- 1$ to the left of $c$ .

$- 1 \cdot c x^{- 2}$

Rewrite $- 1 c$ as $- c$ .

$- c x^{- 2}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- c \frac{1}{x^{2}}$

Combine $\frac{1}{x^{2}}$ and $c$ .

$- \frac{c}{x^{2}}$

Find the Derivative – d/dx c/x

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