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Popular Calculus >

derivative of (24/((x-1)^5))

Solution

\frac{d}{d x} (\frac{24}{( x - 1 ) ^{5}})

Solution

- \frac{120}{( x - 1 ) ^{6}}

Solution steps

\frac{d}{d x} (\frac{24}{( x - 1 ) ^{5}})

Take the constant out:

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

= 24 \frac{d}{d x} (\frac{1}{( x - 1 ) ^{5}})

Apply exponent rule:

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

= 24 \frac{d}{d x} ((x - 1)^{- 5})

Apply the chain rule:

- \frac{5}{( x - 1 ) ^{6}} \frac{d}{d x} (x - 1)

= - \frac{5}{( x - 1 ) ^{6}} \frac{d}{d x} (x - 1)

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

= 24 (- \frac{5}{( x - 1 ) ^{6}} \cdot 1)

Simplify

24 (- \frac{5}{( x - 1 ) ^{6}} \cdot 1) : - \frac{120}{( x - 1 ) ^{6}}

= - \frac{120}{( x - 1 ) ^{6}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (24/((x-1)^5)) ?
The derivative of (24/((x-1)^5)) is -(120)/((x-1)^6)
What is the first derivative of (24/((x-1)^5)) ?
The first derivative of (24/((x-1)^5)) is -(120)/((x-1)^6)