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Popular >

derivative of ln((x+2/(x-1)))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of y=(x+2^x)/(cos(pix))derivative of

y = \frac{x + 2 ^{x}}{cos ( π x )}

derivative of ln(arctan(x))derivative of

ln (arctan (x))

(dy)/(dx)=2+1/x ,y(1)=5

\frac{d y}{d x} = 2 + \frac{1}{x}, y (1) = 5

y^'+2xy=2x^3,y(0)=2

y^{^{'}} + 2 x y = 2 x^{3}, y (0) = 2

inverse oflaplace-(1.25)/(s+2)inverse laplace

- \frac{1.25}{s + 2}

Frequently Asked Questions (FAQ)

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