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

The derivative of ((3x^2-5)/((2x^2+1))) is (26x)/((2x^2+1)^2)

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

The first derivative of ((3x^2-5)/((2x^2+1))) is (26x)/((2x^2+1)^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{( 3 x ^{2} - 5 )}{( 2 x ^{2} + 1 )})

\frac{26 x}{( 2 x ^{2} + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

= \frac{6 x ( 2 x ^{2} + 1 ) - 4 x ( 3 x ^{2} - 5 )}{( 2 x ^{2} + 1 ) ^{2}}

Expand

6 x (2 x^{2} + 1) - 4 x (3 x^{2} - 5) : 26 x

= \frac{26 x}{( 2 x ^{2} + 1 ) ^{2}}

f (x) = e^{x^{4}}

6 x \frac{d y}{d x} = 2 x e^{x} - 6 y + 6 x^{2}

\frac{\partial}{\partial x} (ln (x + 2))

\int x^{2} e^{5 x} d x

8 e^{- x} + e^{3 x}

What is the derivative of ((3x^2-5)/((2x^2+1))) ?
The derivative of ((3x^2-5)/((2x^2+1))) is (26x)/((2x^2+1)^2)
What is the first derivative of ((3x^2-5)/((2x^2+1))) ?
The first derivative of ((3x^2-5)/((2x^2+1))) is (26x)/((2x^2+1)^2)