en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (20/(x^6))

Solution

\frac{d}{d x} (\frac{20}{x ^{6}})

Solution

- \frac{120}{x ^{7}}

Solution steps

\frac{d}{d x} (\frac{20}{x ^{6}})

Take the constant out:

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

= 20 \frac{d}{d x} (\frac{1}{x ^{6}})

Apply exponent rule:

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

= 20 \frac{d}{d x} (x^{- 6})

Apply the Power Rule:

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

= 20 (- 6 x^{- 6 - 1})

Simplify

20 (- 6 x^{- 6 - 1}) : - \frac{120}{x ^{7}}

= - \frac{120}{x ^{7}}

Popular Examples

(d^2y)/(dx^2)+5(dy)/(dx)+6y=12e^x

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = 12 e^{x}

sum from n=1 to infinity of (5+n)/(n!)

n = 1 \sum \infty \frac{5 + n}{n !}

y^{^{'}} + 100 y = 0

sum from n=1 to infinity of 2^n*3^{-n}

n = 1 \sum \infty 2^{n} \cdot 3^{- n}

y = 3 cos (x^{2} - 1)

Frequently Asked Questions (FAQ)

What is the derivative of (20/(x^6)) ?
The derivative of (20/(x^6)) is -(120)/(x^7)
What is the first derivative of (20/(x^6)) ?
The first derivative of (20/(x^6)) is -(120)/(x^7)