en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ((5-x^{-2})/2)

Solution

\frac{d}{d x} (\frac{( 5 - x ) ^{- 2}}{2})

Solution

\frac{1}{( 5 - x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{( 5 - x ) ^{- 2}}{2})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} ((5 - x)^{- 2})

Apply the chain rule:

- \frac{2}{( 5 - x ) ^{3}} \frac{d}{d x} (5 - x)

= - \frac{2}{( 5 - x ) ^{3}} \frac{d}{d x} (5 - x)

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

= \frac{1}{2} (- \frac{2}{( 5 - x ) ^{3}} (- 1))

Simplify

\frac{1}{2} (- \frac{2}{( 5 - x ) ^{3}} (- 1)) : \frac{1}{( 5 - x ) ^{3}}

= \frac{1}{( 5 - x ) ^{3}}

Popular Examples

derivative of 0.2x^2

\frac{d}{d x} (0.2 x^{2})

(d^2)/(dx^2)(14x^3-36x^2)

\frac{d ^{2}}{d x ^{2}} (14 x^{3} - 36 x^{2})

(dQ)/(dt)= 12/5-3Q

\frac{d Q}{d t} = \frac{12}{5} - 3 Q

derivative of 1+sqrt(3x)

\frac{d}{d x} (1 + 3 x)

(\partial)/(\partial y)(xln(1+x+y))

\frac{\partial}{\partial y} (x ln (1 + x + y))

Frequently Asked Questions (FAQ)

What is the derivative of ((5-x^{-2})/2) ?
The derivative of ((5-x^{-2})/2) is 1/((5-x)^3)
What is the first derivative of ((5-x^{-2})/2) ?
The first derivative of ((5-x^{-2})/2) is 1/((5-x)^3)