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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{2 x ^{3} - 27 x}{( 9 - x ^{2} ) 9 - x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (- 2 x^{2} + 9) = - 4 x

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

= \frac{( - 4 x ) 9 - x ^{2} - ( - \frac{x}{9 - x ^{2}} ) ( - 2 x ^{2} + 9 )}{( 9 - x ^{2} ) ^{2}}

Simplify

\frac{( - 4 x ) 9 - x ^{2} - ( - \frac{x}{9 - x ^{2}} ) ( - 2 x ^{2} + 9 )}{( 9 - x ^{2} ) ^{2}} : \frac{2 x ^{3} - 27 x}{( 9 - x ^{2} ) 9 - x ^{2}}

= \frac{2 x ^{3} - 27 x}{( 9 - x ^{2} ) 9 - x ^{2}}

\int_{7}^{8} (\frac{1}{x ^{2}} - 1) d x

(\frac{ln ( x )}{x ^{2}})^{^{'}}

\frac{\partial}{\partial x} (cos^{7} (x^{9} y^{5}))

y = \frac{4 - x e ^{x}}{x + e ^{x}}

\int x^{2} \frac{1}{x} d x

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