What is the derivative of ((x+1/(x-1))^7) ?

The derivative of ((x+1/(x-1))^7) is -(14(x+1)^6)/((x-1)^8)

What is the first derivative of ((x+1/(x-1))^7) ?

The first derivative of ((x+1/(x-1))^7) is -(14(x+1)^6)/((x-1)^8)

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

- \frac{14 ( x + 1 ) ^{6}}{( x - 1 ) ^{8}}

Solution steps

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

Apply the chain rule:

7 (\frac{x + 1}{x - 1})^{6} \frac{d}{d x} (\frac{x + 1}{x - 1})

= 7 (\frac{x + 1}{x - 1})^{6} \frac{d}{d x} (\frac{x + 1}{x - 1})

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

= 7 (\frac{x + 1}{x - 1})^{6} (- \frac{2}{( x - 1 ) ^{2}})

Simplify

7 (\frac{x + 1}{x - 1})^{6} (- \frac{2}{( x - 1 ) ^{2}}) : - \frac{14 ( x + 1 ) ^{6}}{( x - 1 ) ^{8}}

= - \frac{14 ( x + 1 ) ^{6}}{( x - 1 ) ^{8}}

\frac{\partial}{\partial x} (ln (x y^{2} z^{3}))

\frac{d}{d x} (7 cos (3 x))

y (θ) = 4 sin (θ) - 3 cos (θ)

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

\int 15 e^{- 5 t} d t

What is the derivative of ((x+1/(x-1))^7) ?
The derivative of ((x+1/(x-1))^7) is -(14(x+1)^6)/((x-1)^8)
What is the first derivative of ((x+1/(x-1))^7) ?
The first derivative of ((x+1/(x-1))^7) is -(14(x+1)^6)/((x-1)^8)