What is the derivative of (a-b/x ^2) ?

The derivative of (a-b/x ^2) is (2b(ax-b))/(x^3)

What is the first derivative of (a-b/x ^2) ?

The first derivative of (a-b/x ^2) is (2b(ax-b))/(x^3)

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

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

Solution steps

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

Apply the chain rule:

2 (a - \frac{b}{x}) \frac{d}{d x} (a - \frac{b}{x})

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

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

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

Simplify

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

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

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