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)

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derivative of

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

- \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}}

f (x) = e^{4 x} + 4 e^{4 x} x

x \to \infty lim (\frac{ln ^{3} ( x )}{100 3 x})

\int 12 x e^{- 3 x} d x

\frac{d}{d x} (x co x (x))

f (x) = 2 + \frac{1}{x}, (4, 2.25)

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)