What is the derivative of (4x)/(sqrt(x^2+4)) ?

The derivative of (4x)/(sqrt(x^2+4)) is (16)/((x^2+4)sqrt(x^2+4))

What is the first derivative of (4x)/(sqrt(x^2+4)) ?

The first derivative of (4x)/(sqrt(x^2+4)) is (16)/((x^2+4)sqrt(x^2+4))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{4 x}{x ^{2} + 4}

\frac{16}{( x ^{2} + 4 ) x ^{2} + 4}

Solution steps

\frac{d}{d x} (\frac{4 x}{x ^{2} + 4})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (\frac{x}{x ^{2} + 4})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d x}{d x} x ^{2} + 4 - \frac{d}{d x} ( x ^{2} + 4 ) x}{( x ^{2} + 4 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 4) = \frac{x}{x ^{2} + 4}

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

Simplify

4 \cdot \frac{1 \cdot x ^{2} + 4 - \frac{x}{x ^{2} + 4} x}{( x ^{2} + 4 ) ^{2}} : \frac{16}{( x ^{2} + 4 ) x ^{2} + 4}

= \frac{16}{( x ^{2} + 4 ) x ^{2} + 4}

x \to 2 + lim (ln (x - 2))

\int 48 + 2 x - x^{2} d x

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

x \to 0 lim (5 x^{3} + 2 x)

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 6 x - y}

What is the derivative of (4x)/(sqrt(x^2+4)) ?
The derivative of (4x)/(sqrt(x^2+4)) is (16)/((x^2+4)sqrt(x^2+4))
What is the first derivative of (4x)/(sqrt(x^2+4)) ?
The first derivative of (4x)/(sqrt(x^2+4)) is (16)/((x^2+4)sqrt(x^2+4))