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)

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

- \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}}

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)