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Popular >

derivative of (x^2+1)/x

Solution

derivative of

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

Solution

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

Solution steps

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

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

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

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

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

Simplify

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

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

Popular Examples

tangent of f(x)= 5/x ,\at x=4 tangent of

f (x) = \frac{5}{x}, at x = 4

limit as x approaches infinity of ln(x^{4/x})

x \to \infty lim (ln (x^{\frac{4}{x}}))

integral of (x^3+2)/(x^2-1)

\int \frac{x ^{3} + 2}{x ^{2} - 1} d x

y^'-8/x y=(y^5)/(x^{11)}

y^{^{'}} - \frac{8}{x} y = \frac{y ^{5}}{x ^{11}}

integral from 1 to 2 of (2x+x^2)

\int_{1}^{2} (2 x + x^{2}) d x

Frequently Asked Questions (FAQ)

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