What is the derivative of (x+9)/(x^3+x-2) ?

The derivative of (x+9)/(x^3+x-2) is (-2x^3-27x^2-11)/((x^3+x-2)^2)

What is the first derivative of (x+9)/(x^3+x-2) ?

The first derivative of (x+9)/(x^3+x-2) is (-2x^3-27x^2-11)/((x^3+x-2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{x + 9}{x ^{3} + x - 2}

\frac{- 2 x ^{3} - 27 x ^{2} - 11}{( x ^{3} + x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 9}{x ^{3} + x - 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 9 ) ( x ^{3} + x - 2 ) - \frac{d}{d x} ( x ^{3} + x - 2 ) ( x + 9 )}{( x ^{3} + x - 2 ) ^{2}}

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

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

= \frac{1 \cdot ( x ^{3} + x - 2 ) - ( 3 x ^{2} + 1 ) ( x + 9 )}{( x ^{3} + x - 2 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{3} + x - 2 ) - ( 3 x ^{2} + 1 ) ( x + 9 )}{( x ^{3} + x - 2 ) ^{2}} : \frac{- 2 x ^{3} - 27 x ^{2} - 11}{( x ^{3} + x - 2 ) ^{2}}

= \frac{- 2 x ^{3} - 27 x ^{2} - 11}{( x ^{3} + x - 2 ) ^{2}}

\int \frac{24 x}{( 3 x ^{2} + 7 ) ^{3}} d x

\int x^{1} cos (- 5 x) d x

x y^{^{'}} + (x + 1) y = x, y (ln (2)) = 1

x \to 0 lim (4 x + tan (2 x))

\int 13 tan^{3} (x) d x

What is the derivative of (x+9)/(x^3+x-2) ?
The derivative of (x+9)/(x^3+x-2) is (-2x^3-27x^2-11)/((x^3+x-2)^2)
What is the first derivative of (x+9)/(x^3+x-2) ?
The first derivative of (x+9)/(x^3+x-2) is (-2x^3-27x^2-11)/((x^3+x-2)^2)