What is the derivative of ((6x^2-5)(x^2-6))/(x^2+4) ?

The derivative of ((6x^2-5)(x^2-6))/(x^2+4) is (12x^5+96x^3-388x)/((x^2+4)^2)

What is the first derivative of ((6x^2-5)(x^2-6))/(x^2+4) ?

The first derivative of ((6x^2-5)(x^2-6))/(x^2+4) is (12x^5+96x^3-388x)/((x^2+4)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{( 6 x ^{2} - 5 ) ( x ^{2} - 6 )}{x ^{2} + 4}

\frac{12 x ^{5} + 96 x ^{3} - 388 x}{( x ^{2} + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( 6 x ^{2} - 5 ) ( x ^{2} - 6 )}{x ^{2} + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( 6 x ^{2} - 5 ) ( x ^{2} - 6 ) ) ( x ^{2} + 4 ) - \frac{d}{d x} ( x ^{2} + 4 ) ( 6 x ^{2} - 5 ) ( x ^{2} - 6 )}{( x ^{2} + 4 ) ^{2}}

\frac{d}{d x} ((6 x^{2} - 5) (x^{2} - 6)) = 24 x^{3} - 82 x

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

= \frac{( 24 x ^{3} - 82 x ) ( x ^{2} + 4 ) - 2 x ( 6 x ^{2} - 5 ) ( x ^{2} - 6 )}{( x ^{2} + 4 ) ^{2}}

Expand

(24 x^{3} - 82 x) (x^{2} + 4) - 2 x (6 x^{2} - 5) (x^{2} - 6) : 12 x^{5} + 96 x^{3} - 388 x

= \frac{12 x ^{5} + 96 x ^{3} - 388 x}{( x ^{2} + 4 ) ^{2}}

y^{^{''}} - \frac{2 3}{3} y^{^{'}} + \frac{2}{9} = 0

\int_{0}^{2} (2 x - 1)^{2} d x

\int sec (3 t) tan (3 t) d t

y^{^{''}} + 5 y^{^{'}} + 10 y = 510 e^{2 t} cos (6 t)

\int \frac{x ^{2}}{6 x - x ^{2}} d x

What is the derivative of ((6x^2-5)(x^2-6))/(x^2+4) ?
The derivative of ((6x^2-5)(x^2-6))/(x^2+4) is (12x^5+96x^3-388x)/((x^2+4)^2)
What is the first derivative of ((6x^2-5)(x^2-6))/(x^2+4) ?
The first derivative of ((6x^2-5)(x^2-6))/(x^2+4) is (12x^5+96x^3-388x)/((x^2+4)^2)