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Popular >

derivative of (sqrt(x^2+1)/x)

Solution

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

Solution

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

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

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

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

Simplify

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

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

Popular Examples

derivative of 1/(x^3+2)

\frac{d}{d x} (\frac{1}{x ^{3} + 2})

limit as x approaches 2 of x^3-2x^2+x-3

x \to 2 lim (x^{3} - 2 x^{2} + x - 3)

derivative of (2-3x^2)^4(x^7+3)^3 derivative of

(2 - 3 x^{2})^{4} (x^{7} + 3)^{3}

derivative of f(x)=(sqrt(x))/4 derivative of

f (x) = \frac{x}{4}

derivative of 2+sqrt(5x)

\frac{d}{d x} (2 + 5 x)

Frequently Asked Questions (FAQ)

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