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

The derivative of sin(1/(x-1)) is -(cos(1/(x-1)))/((x-1)^2)

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

The first derivative of sin(1/(x-1)) is -(cos(1/(x-1)))/((x-1)^2)

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

- \frac{cos ( \frac{1}{x - 1} )}{( x - 1 ) ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{''}} + 4 y = 3 sin (2 t)

5^{x^{5}}

\int \frac{1}{ln ( 2 x )} d x

2 y = 5 x, y = 3, 2 y + 2 x = 7

\int x (3^{x}) d x

What is the derivative of sin(1/(x-1)) ?
The derivative of sin(1/(x-1)) is -(cos(1/(x-1)))/((x-1)^2)
What is the first derivative of sin(1/(x-1)) ?
The first derivative of sin(1/(x-1)) is -(cos(1/(x-1)))/((x-1)^2)