What is the derivative of sqrt(4+cot^2(x)) ?

The derivative of sqrt(4+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(4+cot^2(x)))

What is the first derivative of sqrt(4+cot^2(x)) ?

The first derivative of sqrt(4+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(4+cot^2(x)))

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derivative of

4 + cot^{2} (x)

- \frac{csc ^{2} ( x ) cot ( x )}{4 + cot ^{2} ( x )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 + cot^{2} (x)) = - 2 csc^{2} (x) cot (x)

= \frac{1}{2 4 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x))

Simplify

\frac{1}{2 4 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x)) : - \frac{csc ^{2} ( x ) cot ( x )}{4 + cot ^{2} ( x )}

= - \frac{csc ^{2} ( x ) cot ( x )}{4 + cot ^{2} ( x )}

x + 5

\int_{0}^{N} e^{- s t} e^{5 t} d t

x \to 2 lim (- x + 6)

h \to 0 lim (2 + h)

\int e^{r} r + e^{r} d r

What is the derivative of sqrt(4+cot^2(x)) ?
The derivative of sqrt(4+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(4+cot^2(x)))
What is the first derivative of sqrt(4+cot^2(x)) ?
The first derivative of sqrt(4+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(4+cot^2(x)))