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}

y = \frac{e ^{x}}{x + e ^{x}}

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

\frac{d}{d x} (x^{3} (x^{2} + 4 + \frac{1}{x}))

\frac{d}{d x} (x^{2} + 2 y^{2} + z^{2} - 6 x + 3 y - 2 z + 5)

y^{^{''}} - 6 y^{^{'}} + 0 y = 0

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))