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Popular >

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

Solution

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

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\int x \cdot e^{x} d x

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derivative of sqrt(81+x^2)

\frac{d}{d x} (81 + x^{2})

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\frac{d}{d x} (x arcsin (\frac{x}{4}) + 16 - x^{2})

integral of 45(1+sqrt(x))

\int 45 (1 + x) d x

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)