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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (1-3x^2^{1/(sin^2(x))})

\frac{d}{d x} ((1 - 3 x^{2})^{\frac{1}{s i n ^{2} ( x )}})

integral of [xsqrt((x-1))]

\int [x (x - 1)] d x

limit as x approaches 1+of 4/(x^3-1)

x \to 1 + lim (\frac{4}{x ^{3} - 1})

integral of 3x^2(x^3+4)^4

\int 3 x^{2} (x^{3} + 4)^{4} d x

f(x)=ln(sin(2x))

f (x) = ln (sin (2 x))

Frequently Asked Questions (FAQ)

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