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Popular >

derivative of (x^2-1)/(x^2)

Solution

derivative of

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

Solution

\frac{2}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

= \frac{2}{x ^{3}}

Popular Examples

limit as x approaches 0 of ((4+x)^{-1}-4^{-1})/x

x \to 0 lim (\frac{( 4 + x ) ^{- 1} - 4 ^{- 1}}{x})

derivative of g(t)= 5/(sqrt(t))derivative of

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derivative of 2^2 derivative of

2^{2}

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\int x arctan^{2} (x) d x

(\partial ^2)/(\partial x\partial y)(xy+8/x+8/y)

\frac{\partial ^{2}}{\partial x \partial y} (x y + \frac{8}{x} + \frac{8}{y})

Frequently Asked Questions (FAQ)

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