What is the derivative of (9x)/(sqrt(x^2+5)) ?

The derivative of (9x)/(sqrt(x^2+5)) is (45)/((x^2+5)sqrt(x^2+5))

What is the first derivative of (9x)/(sqrt(x^2+5)) ?

The first derivative of (9x)/(sqrt(x^2+5)) is (45)/((x^2+5)sqrt(x^2+5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{9 x}{x ^{2} + 5}

\frac{45}{( x ^{2} + 5 ) x ^{2} + 5}

Solution steps

\frac{d}{d x} (\frac{9 x}{x ^{2} + 5})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{x}{x ^{2} + 5})

Apply the Quotient Rule:

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

= 9 \cdot \frac{\frac{d x}{d x} x ^{2} + 5 - \frac{d}{d x} ( x ^{2} + 5 ) x}{( x ^{2} + 5 ) ^{2}}

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

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

= 9 \cdot \frac{1 \cdot x ^{2} + 5 - \frac{x}{x ^{2} + 5} x}{( x ^{2} + 5 ) ^{2}}

Simplify

9 \cdot \frac{1 \cdot x ^{2} + 5 - \frac{x}{x ^{2} + 5} x}{( x ^{2} + 5 ) ^{2}} : \frac{45}{( x ^{2} + 5 ) x ^{2} + 5}

= \frac{45}{( x ^{2} + 5 ) x ^{2} + 5}

x \to \frac{π}{2} lim (\frac{tan ( 2 x )}{x - \frac{π}{2}})

\frac{d ^{2} y}{d x ^{2}} + 4 y = 2 sin (3 x)

y^{^{'}} = k + b cos (2 π t)

\frac{d}{d x} (2 x^{3} + 5)

\frac{d}{d x} (arcsin^{2} (x))

What is the derivative of (9x)/(sqrt(x^2+5)) ?
The derivative of (9x)/(sqrt(x^2+5)) is (45)/((x^2+5)sqrt(x^2+5))
What is the first derivative of (9x)/(sqrt(x^2+5)) ?
The first derivative of (9x)/(sqrt(x^2+5)) is (45)/((x^2+5)sqrt(x^2+5))