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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\frac{d}{d x} ((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}}

x y^{3}

\frac{4 2}{3} x^{\frac{3}{2}} - 1

\frac{1}{1 + x ^{2}}

\int \frac{27 x ^{2}}{x ^{2} - 4} d x

\int x 3 x + 5 d x

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)