What is the derivative of (7x+1)/(2sqrt(x)-3) ?

The derivative of (7x+1)/(2sqrt(x)-3) is (7x-21sqrt(x)-1)/(sqrt(x)(2\sqrt{x)-3)^2}

What is the first derivative of (7x+1)/(2sqrt(x)-3) ?

The first derivative of (7x+1)/(2sqrt(x)-3) is (7x-21sqrt(x)-1)/(sqrt(x)(2\sqrt{x)-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{7 x + 1}{2 x - 3}

\frac{7 x - 21 x - 1}{x ( 2 x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 x + 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} ( 7 x + 1 ) ( 2 x - 3 ) - \frac{d}{d x} ( 2 x - 3 ) ( 7 x + 1 )}{( 2 x - 3 ) ^{2}}

\frac{d}{d x} (7 x + 1) = 7

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

= \frac{7 ( 2 x - 3 ) - \frac{1}{x} ( 7 x + 1 )}{( 2 x - 3 ) ^{2}}

Simplify

\frac{7 ( 2 x - 3 ) - \frac{1}{x} ( 7 x + 1 )}{( 2 x - 3 ) ^{2}} : \frac{7 x - 21 x - 1}{x ( 2 x - 3 ) ^{2}}

= \frac{7 x - 21 x - 1}{x ( 2 x - 3 ) ^{2}}

\int_{0}^{1} x^{3} ln (x^{8}) d x

f (x) = \frac{x}{x + 3}, at x = 1

\frac{d}{d x} (cos^{2} (4 π x))

f (x) = x^{2} + 2

\frac{d y}{d t} = y (8 - y), y (0) = 9

What is the derivative of (7x+1)/(2sqrt(x)-3) ?
The derivative of (7x+1)/(2sqrt(x)-3) is (7x-21sqrt(x)-1)/(sqrt(x)(2\sqrt{x)-3)^2}
What is the first derivative of (7x+1)/(2sqrt(x)-3) ?
The first derivative of (7x+1)/(2sqrt(x)-3) is (7x-21sqrt(x)-1)/(sqrt(x)(2\sqrt{x)-3)^2}