What is the derivative of 5cot(2/x) ?

The derivative of 5cot(2/x) is (10csc^2(2/x))/(x^2)

What is the first derivative of 5cot(2/x) ?

The first derivative of 5cot(2/x) is (10csc^2(2/x))/(x^2)

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\frac{d}{d x} (5 cot (\frac{2}{x}))

\frac{10 csc ^{2} ( \frac{2}{x} )}{x ^{2}}

Solution steps

\frac{d}{d x} (5 cot (\frac{2}{x}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (cot (\frac{2}{x}))

Apply the chain rule:

- csc^{2} (\frac{2}{x}) \frac{d}{d x} (\frac{2}{x})

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

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

= 5 (- csc^{2} (\frac{2}{x}) (- \frac{2}{x ^{2}}))

Simplify

5 (- csc^{2} (\frac{2}{x}) (- \frac{2}{x ^{2}})) : \frac{10 csc ^{2} ( \frac{2}{x} )}{x ^{2}}

= \frac{10 csc ^{2} ( \frac{2}{x} )}{x ^{2}}

\int 2^{c o s (x)} sin (x) d x

\int_{0}^{\frac{π}{4}} tan (x) d x

\frac{8}{3 s ^{2} + 12} + \frac{3}{s ^{2} - 49}

\int 1 + 64 x^{2} d x

\int e^{2} cos (x) d x

What is the derivative of 5cot(2/x) ?
The derivative of 5cot(2/x) is (10csc^2(2/x))/(x^2)
What is the first derivative of 5cot(2/x) ?
The first derivative of 5cot(2/x) is (10csc^2(2/x))/(x^2)