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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\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}}

(- 4, - 9), (7, 7)

\frac{\partial}{\partial x} (x y cos (6 yz))

\frac{\partial}{\partial x} (- x^{3})

\frac{\partial}{\partial x} (- \frac{1}{2} x - 3 y + 1)

x \to 1 lim (3 + x^{2})

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)