What is the derivative of x/(sqrt(5+x^2)) ?

The derivative of x/(sqrt(5+x^2)) is 5/((5+x^2)sqrt(5+x^2))

What is the first derivative of x/(sqrt(5+x^2)) ?

The first derivative of x/(sqrt(5+x^2)) is 5/((5+x^2)sqrt(5+x^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}{5 + x ^{2}})

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

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} 5 + x ^{2} - \frac{d}{d x} ( 5 + x ^{2} ) x}{( 5 + x ^{2} ) ^{2}}

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

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

= \frac{1 \cdot 5 + x ^{2} - \frac{x}{5 + x ^{2}} x}{( 5 + x ^{2} ) ^{2}}

Simplify

\frac{1 \cdot 5 + x ^{2} - \frac{x}{5 + x ^{2}} x}{( 5 + x ^{2} ) ^{2}} : \frac{5}{( 5 + x ^{2} ) 5 + x ^{2}}

= \frac{5}{( 5 + x ^{2} ) 5 + x ^{2}}

y^{^{''}} + 9 y = 4 tan (3 x)

y = ln^{2} (x + 3)

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

2 y^{^{''}} + 12 y^{^{'}} + 50 y = 0, y (0) = 0, y^{^{'}} (0) = - 8

y = x + 8, (8, 4)

What is the derivative of x/(sqrt(5+x^2)) ?
The derivative of x/(sqrt(5+x^2)) is 5/((5+x^2)sqrt(5+x^2))
What is the first derivative of x/(sqrt(5+x^2)) ?
The first derivative of x/(sqrt(5+x^2)) is 5/((5+x^2)sqrt(5+x^2))