What is the derivative of cot(sqrt(x)) ?

The derivative of cot(sqrt(x)) is -(csc^2(sqrt(x)))/(2sqrt(x))

What is the first derivative of cot(sqrt(x)) ?

The first derivative of cot(sqrt(x)) is -(csc^2(sqrt(x)))/(2sqrt(x))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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