What is the derivative of ((x^2-5x))/((9-x^3)^{1/2)} ?

The derivative of ((x^2-5x))/((9-x^3)^{1/2)} is (-x^4-5x^3+36x-90)/(2(9-x^3)^{3/2)}

What is the first derivative of ((x^2-5x))/((9-x^3)^{1/2)} ?

The first derivative of ((x^2-5x))/((9-x^3)^{1/2)} is (-x^4-5x^3+36x-90)/(2(9-x^3)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{( x ^{2} - 5 x )}{( 9 - x ^{3} ) ^{\frac{1}{2}}}

\frac{- x ^{4} - 5 x ^{3} + 36 x - 90}{2 ( 9 - x ^{3} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 5 x}{( 9 - x ^{3} ) ^{\frac{1}{2}}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 5 x ) ( 9 - x ^{3} ) ^{\frac{1}{2}} - \frac{d}{d x} ( ( 9 - x ^{3} ) ^{\frac{1}{2}} ) ( x ^{2} - 5 x )}{( ( 9 - x ^{3} ) ^{\frac{1}{2}} ) ^{2}}

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

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

= \frac{( 2 x - 5 ) ( 9 - x ^{3} ) ^{\frac{1}{2}} - ( - \frac{3 x ^{2}}{2 ( 9 - x ^{3} ) ^{\frac{1}{2}}} ) ( x ^{2} - 5 x )}{( ( 9 - x ^{3} ) ^{\frac{1}{2}} ) ^{2}}

Simplify

\frac{( 2 x - 5 ) ( 9 - x ^{3} ) ^{\frac{1}{2}} - ( - \frac{3 x ^{2}}{2 ( 9 - x ^{3} ) ^{\frac{1}{2}}} ) ( x ^{2} - 5 x )}{( ( 9 - x ^{3} ) ^{\frac{1}{2}} ) ^{2}} : \frac{- x ^{4} - 5 x ^{3} + 36 x - 90}{2 ( 9 - x ^{3} ) ^{\frac{3}{2}}}

= \frac{- x ^{4} - 5 x ^{3} + 36 x - 90}{2 ( 9 - x ^{3} ) ^{\frac{3}{2}}}

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

n = 1 \sum \infty \frac{2 ^{n}}{100}

\int x^{2} cos (x + 1) d x

\frac{\partial}{\partial y} (- y sin (x y))

\int cos (2 a x) d x

What is the derivative of ((x^2-5x))/((9-x^3)^{1/2)} ?
The derivative of ((x^2-5x))/((9-x^3)^{1/2)} is (-x^4-5x^3+36x-90)/(2(9-x^3)^{3/2)}
What is the first derivative of ((x^2-5x))/((9-x^3)^{1/2)} ?
The first derivative of ((x^2-5x))/((9-x^3)^{1/2)} is (-x^4-5x^3+36x-90)/(2(9-x^3)^{3/2)}