en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (a+b/(x^2)^3)

Solution

\frac{d}{d x} ((a + \frac{b}{x ^{2}})^{3})

Solution

- \frac{6 b ( a x ^{2} + b ) ^{2}}{x ^{7}}

Solution steps

\frac{d}{d x} ((a + \frac{b}{x ^{2}})^{3})

Apply the chain rule:

3 (a + \frac{b}{x ^{2}})^{2} \frac{d}{d x} (a + \frac{b}{x ^{2}})

= 3 (a + \frac{b}{x ^{2}})^{2} \frac{d}{d x} (a + \frac{b}{x ^{2}})

\frac{d}{d x} (a + \frac{b}{x ^{2}}) = - \frac{2 b}{x ^{3}}

= 3 (a + \frac{b}{x ^{2}})^{2} (- \frac{2 b}{x ^{3}})

Simplify

3 (a + \frac{b}{x ^{2}})^{2} (- \frac{2 b}{x ^{3}}) : - \frac{6 b ( a x ^{2} + b ) ^{2}}{x ^{7}}

= - \frac{6 b ( a x ^{2} + b ) ^{2}}{x ^{7}}

Popular Examples

derivative of sin(x)ln(x)derivative of

sin (x) ln (x)

derivative of f(x)=2sin^5(sqrt(x))derivative of

f (x) = 2 sin^{5} (x)

derivative of xsin(x^2)derivative of

x sin (x^{2})

y^{''}(s)-4y^'(s)+3y(s)=-e^{-s},y(0)=0,y^'(0)=0

y^{^{''}} (s) - 4 y^{^{'}} (s) + 3 y (s) = - e^{- s}, y (0) = 0, y^{^{'}} (0) = 0

derivative of arcsec(2x+2)derivative of

arcsec (2 x + 2)

Frequently Asked Questions (FAQ)

What is the derivative of (a+b/(x^2)^3) ?
The derivative of (a+b/(x^2)^3) is -(6b(ax^2+b)^2)/(x^7)
What is the first derivative of (a+b/(x^2)^3) ?
The first derivative of (a+b/(x^2)^3) is -(6b(ax^2+b)^2)/(x^7)