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Popular >

derivative of y=(x^2-4)/x

Solution

derivative of

y = \frac{x ^{2} - 4}{x}

Solution

\frac{x ^{2} + 4}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 4 ) x - \frac{d x}{d x} ( x ^{2} - 4 )}{x ^{2}}

\frac{d}{d x} (x^{2} - 4) = 2 x

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

= \frac{2 xx - 1 \cdot ( x ^{2} - 4 )}{x ^{2}}

Simplify

\frac{2 xx - 1 \cdot ( x ^{2} - 4 )}{x ^{2}} : \frac{x ^{2} + 4}{x ^{2}}

= \frac{x ^{2} + 4}{x ^{2}}

Popular Examples

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\frac{1}{s ^{2} + s ^{2}}

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x \to 6 lim (cos (x \cdot π))

(\partial)/(\partial x)(I/(2x))

\frac{\partial}{\partial x} (\frac{I}{2 x})

(\partial)/(\partial x)(2x^2e^y)

\frac{\partial}{\partial x} (2 x^{2} e^{y})

derivative of (x^2+4^{-2})

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

Frequently Asked Questions (FAQ)

What is the derivative of y=(x^2-4)/x ?
The derivative of y=(x^2-4)/x is (x^2+4)/(x^2)
What is the first derivative of y=(x^2-4)/x ?
The first derivative of y=(x^2-4)/x is (x^2+4)/(x^2)