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Popular >

derivative of (1-x^2/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

Popular Examples

derivative of x^2-x^3+3

\frac{d}{d x} (x^{2} - x^{3} + 3)

integral of (e^{ln^2(x)})/x ln(x)

\int \frac{e ^{l n^{2} (x)}}{x} ln (x) d x

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y = \frac{8}{x - 7}

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\frac{d}{d x} (2 x + cos (x))

integral of x^{27}e^{-x^{28}}

\int x^{27} e^{- x^{28}} d x

Frequently Asked Questions (FAQ)

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