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

The derivative of (sqrt(x)+1/(x^2+1)) is (-3x^2-4xsqrt(x)+1)/(2sqrt(x)(x^2+1)^2)

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

The first derivative of (sqrt(x)+1/(x^2+1)) is (-3x^2-4xsqrt(x)+1)/(2sqrt(x)(x^2+1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{- 3 x ^{2} - 4 x x + 1}{2 x ( x ^{2} + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{\frac{1}{2 x} ( x ^{2} + 1 ) - 2 x ( x + 1 )}{( x ^{2} + 1 ) ^{2}} : \frac{- 3 x ^{2} - 4 x x + 1}{2 x ( x ^{2} + 1 ) ^{2}}

= \frac{- 3 x ^{2} - 4 x x + 1}{2 x ( x ^{2} + 1 ) ^{2}}

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

(\frac{cos ( x )}{sin ( x )})^{^{'}}

\frac{d}{d x} (∣ x - 3 ∣)

y = sin (3 x) + sin^{2} (3 x), (0, 0)

x \to \infty lim (2, x)

What is the derivative of (sqrt(x)+1/(x^2+1)) ?
The derivative of (sqrt(x)+1/(x^2+1)) is (-3x^2-4xsqrt(x)+1)/(2sqrt(x)(x^2+1)^2)
What is the first derivative of (sqrt(x)+1/(x^2+1)) ?
The first derivative of (sqrt(x)+1/(x^2+1)) is (-3x^2-4xsqrt(x)+1)/(2sqrt(x)(x^2+1)^2)