What is the derivative of (x^2+6x/(10-x^2)) ?

The derivative of (x^2+6x/(10-x^2)) is (6x^2+20x+60)/((10-x^2)^2)

What is the first derivative of (x^2+6x/(10-x^2)) ?

The first derivative of (x^2+6x/(10-x^2)) is (6x^2+20x+60)/((10-x^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{x ^{2} + 6 x}{10 - x ^{2}})

\frac{6 x ^{2} + 20 x + 60}{( 10 - x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 6 x}{10 - x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 6 x ) ( 10 - x ^{2} ) - \frac{d}{d x} ( 10 - x ^{2} ) ( x ^{2} + 6 x )}{( 10 - x ^{2} ) ^{2}}

\frac{d}{d x} (x^{2} + 6 x) = 2 x + 6

\frac{d}{d x} (10 - x^{2}) = - 2 x

= \frac{( 2 x + 6 ) ( 10 - x ^{2} ) - ( - 2 x ) ( x ^{2} + 6 x )}{( 10 - x ^{2} ) ^{2}}

Simplify

\frac{( 2 x + 6 ) ( 10 - x ^{2} ) - ( - 2 x ) ( x ^{2} + 6 x )}{( 10 - x ^{2} ) ^{2}} : \frac{6 x ^{2} + 20 x + 60}{( 10 - x ^{2} ) ^{2}}

= \frac{6 x ^{2} + 20 x + 60}{( 10 - x ^{2} ) ^{2}}

y^{^{''}} - 7 y^{^{'}} + 10 y = - sin (3 t)

y = x^{2} + 2 x - 11, y = 3, [3, 5]

\frac{\partial}{\partial x} (4 x sin (7 x^{2} y))

f (x) = 3 x^{2} - 5 x

f (x) = - \frac{4}{3} x^{- \frac{5}{2}}, at x = 4

What is the derivative of (x^2+6x/(10-x^2)) ?
The derivative of (x^2+6x/(10-x^2)) is (6x^2+20x+60)/((10-x^2)^2)
What is the first derivative of (x^2+6x/(10-x^2)) ?
The first derivative of (x^2+6x/(10-x^2)) is (6x^2+20x+60)/((10-x^2)^2)