What is the derivative of f(x)=(sqrt(x^2+1))/x ?

The derivative of f(x)=(sqrt(x^2+1))/x is -1/(x^2sqrt(x^2+1))

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

The first derivative of f(x)=(sqrt(x^2+1))/x is -1/(x^2sqrt(x^2+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

- \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}

n = 1 \sum \infty \frac{5}{n ( n + 2 )}

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

y^{^{'}} + 6 y = e^{t}

\int \frac{5}{3 - 2 cos ( x )} d x

\frac{\partial}{\partial x} (x cos (\frac{y}{z}))

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