What is the derivative of sqrt(2+cot^2(x)) ?

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

What is the first derivative of sqrt(2+cot^2(x)) ?

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

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\frac{d}{d x} (2 + cot^{2} (x))

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

Solution steps

\frac{d}{d x} (2 + cot^{2} (x))

Apply the chain rule:

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

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

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

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

Simplify

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

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

x^{2} - 5 x + 1, (- 3, 6)

\int \frac{1}{( sin ( x ) ) ^{5} ( cos ( x ) ) ^{5}} d x

\frac{1}{19 s ^{2} + 5 s + 19990}

\frac{\partial}{\partial s} (arctan (rs))

y^{^{''}} + 6 y^{^{'}} + 45 y = 0

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