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

The derivative of (x^2+1/(2x-3)) is (2x^2-6x-2)/((2x-3)^2)

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

The first derivative of (x^2+1/(2x-3)) is (2x^2-6x-2)/((2x-3)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

What is the derivative of (x^2+1/(2x-3)) ?
The derivative of (x^2+1/(2x-3)) is (2x^2-6x-2)/((2x-3)^2)
What is the first derivative of (x^2+1/(2x-3)) ?
The first derivative of (x^2+1/(2x-3)) is (2x^2-6x-2)/((2x-3)^2)