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

The derivative of 1/(sin(1/x)) is (cot(1/x)csc(1/x))/(x^2)

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

The first derivative of 1/(sin(1/x)) is (cot(1/x)csc(1/x))/(x^2)

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

\frac{cot ( \frac{1}{x} ) csc ( \frac{1}{x} )}{x ^{2}}

Solution steps

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

Simplify

\frac{1}{sin ( \frac{1}{x} )} : csc (\frac{1}{x})

= \frac{d}{d x} (csc (\frac{1}{x}))

Apply the chain rule:

- cot (\frac{1}{x}) csc (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

= - cot (\frac{1}{x}) csc (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

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

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

Simplify

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

= \frac{cot ( \frac{1}{x} ) csc ( \frac{1}{x} )}{x ^{2}}

\frac{d}{d x} (\frac{4 x}{5 - cot ( x )})

\int \frac{e ^{t} + 2 e ^{2 t}}{e ^{3 t}} d t

\frac{\partial}{\partial x} (x e^{5 y})

\frac{d}{d x} (3 x^{2} - 4 x)

\frac{\partial}{\partial y} (2 x^{2} y)

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