What is the derivative of f(x)=cx^{-6} ?

The derivative of f(x)=cx^{-6} is -(6c)/(x^7)

What is the first derivative of f(x)=cx^{-6} ?

The first derivative of f(x)=cx^{-6} is -(6c)/(x^7)

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derivative of

f (x) = c x^{- 6}

- \frac{6 c}{x ^{7}}

Solution steps

\frac{d}{d x} (c x^{- 6})

Take the constant out:

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

= c \frac{d}{d x} (x^{- 6})

Apply the Power Rule:

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

= c (- 6 x^{- 6 - 1})

Simplify

c (- 6 x^{- 6 - 1}) : - \frac{6 c}{x ^{7}}

= - \frac{6 c}{x ^{7}}

What is the derivative of f(x)=cx^{-6} ?
The derivative of f(x)=cx^{-6} is -(6c)/(x^7)
What is the first derivative of f(x)=cx^{-6} ?
The first derivative of f(x)=cx^{-6} is -(6c)/(x^7)