What is the derivative of (27)/(x^2+9) ?

The derivative of (27)/(x^2+9) is -(54x)/((x^2+9)^2)

What is the first derivative of (27)/(x^2+9) ?

The first derivative of (27)/(x^2+9) is -(54x)/((x^2+9)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{27}{x ^{2} + 9}

- \frac{54 x}{( x ^{2} + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{27}{x ^{2} + 9})

Take the constant out:

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

= 27 \frac{d}{d x} (\frac{1}{x ^{2} + 9})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 27 \frac{d}{d x} ((x^{2} + 9)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} + 9 ) ^{2}} \frac{d}{d x} (x^{2} + 9)

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

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

= 27 (- \frac{1}{( x ^{2} + 9 ) ^{2}} \cdot 2 x)

Simplify

27 (- \frac{1}{( x ^{2} + 9 ) ^{2}} \cdot 2 x) : - \frac{54 x}{( x ^{2} + 9 ) ^{2}}

= - \frac{54 x}{( x ^{2} + 9 ) ^{2}}

\frac{\partial}{\partial x} (- 2 e^{4 y - x^{2} - y^{2}} x)

x \to \infty lim (x - 6)

(8 cos (π x)), (8 x^{2} - 2), [- 0.5, 0.5]

\frac{\partial}{\partial y} ((x - 4) ln (x y))

θ \to 0 lim (sin (θ))

What is the derivative of (27)/(x^2+9) ?
The derivative of (27)/(x^2+9) is -(54x)/((x^2+9)^2)
What is the first derivative of (27)/(x^2+9) ?
The first derivative of (27)/(x^2+9) is -(54x)/((x^2+9)^2)