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

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

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

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

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derivative of

f (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}}

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