What is the derivative of cot^{1/2}(x) ?

The derivative of cot^{1/2}(x) is -(csc^2(x))/(2sqrt(cot(x)))

What is the first derivative of cot^{1/2}(x) ?

The first derivative of cot^{1/2}(x) is -(csc^2(x))/(2sqrt(cot(x)))

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(4 - x^{2})^{2}

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

y = lo g_{10} (x^{2} + 2 x + 1)

\frac{1}{3 tan ^{3} ( x )}

(x + 2)^{- 4}

What is the derivative of cot^{1/2}(x) ?
The derivative of cot^{1/2}(x) is -(csc^2(x))/(2sqrt(cot(x)))
What is the first derivative of cot^{1/2}(x) ?
The first derivative of cot^{1/2}(x) is -(csc^2(x))/(2sqrt(cot(x)))