What is the derivative of c/x ?

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

What is the first derivative of c/x ?

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

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derivative of

\frac{c}{x}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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