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

The derivative of ln(sqrt((5x+1)/(x^2-3))) is (-5x^2-2x-15)/(2(x^2-3)(5x+1))

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

The first derivative of ln(sqrt((5x+1)/(x^2-3))) is (-5x^2-2x-15)/(2(x^2-3)(5x+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{- 5 x ^{2} - 2 x - 15}{2 ( x ^{2} - 3 ) ( 5 x + 1 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{5 x + 1}{x ^{2} - 3}) = \frac{- 5 x ^{2} - 2 x - 15}{2 5 x + 1 ( x ^{2} - 3 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{5 x + 1}{x ^{2} - 3}} \cdot \frac{- 5 x ^{2} - 2 x - 15}{2 5 x + 1 ( x ^{2} - 3 ) ^{\frac{3}{2}}}

Simplify

\frac{1}{\frac{5 x + 1}{x ^{2} - 3}} \cdot \frac{- 5 x ^{2} - 2 x - 15}{2 5 x + 1 ( x ^{2} - 3 ) ^{\frac{3}{2}}} : \frac{- 5 x ^{2} - 2 x - 15}{2 ( x ^{2} - 3 ) ( 5 x + 1 )}

= \frac{- 5 x ^{2} - 2 x - 15}{2 ( x ^{2} - 3 ) ( 5 x + 1 )}

\frac{3}{x + 3}, at x = 4

y^{^{'}} = \frac{( x ^{3} + y ^{3} )}{3 x y ^{2}}

\frac{y}{x ^{2}} d x + (y - \frac{1}{x}) d y = 0

\frac{\partial}{\partial x} (e^{5 x yz - 9})

\frac{\partial}{\partial y} (\frac{1}{y + 2 z})

What is the derivative of ln(sqrt((5x+1)/(x^2-3))) ?
The derivative of ln(sqrt((5x+1)/(x^2-3))) is (-5x^2-2x-15)/(2(x^2-3)(5x+1))
What is the first derivative of ln(sqrt((5x+1)/(x^2-3))) ?
The first derivative of ln(sqrt((5x+1)/(x^2-3))) is (-5x^2-2x-15)/(2(x^2-3)(5x+1))