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

The derivative of cos((x+1/(x-1))) is (2sin(\frac{x+1)/(x-1))}{(x-1)^2}

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

The first derivative of cos((x+1/(x-1))) is (2sin(\frac{x+1)/(x-1))}{(x-1)^2}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (x in x)

\int \frac{1}{3 + 2 x} d x

\int z^{3} d z

\int \frac{1}{2} x d x

y = \frac{1}{x ^{4}}, (3, \frac{1}{81})

What is the derivative of cos((x+1/(x-1))) ?
The derivative of cos((x+1/(x-1))) is (2sin(\frac{x+1)/(x-1))}{(x-1)^2}
What is the first derivative of cos((x+1/(x-1))) ?
The first derivative of cos((x+1/(x-1))) is (2sin(\frac{x+1)/(x-1))}{(x-1)^2}