What is the derivative of sqrt(5+cot^2(x)) ?

The derivative of sqrt(5+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(5+cot^2(x)))

What is the first derivative of sqrt(5+cot^2(x)) ?

The first derivative of sqrt(5+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(5+cot^2(x)))

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\frac{d}{d x} (5 + cot^{2} (x))

- \frac{csc ^{2} ( x ) cot ( x )}{5 + cot ^{2} ( x )}

Solution steps

\frac{d}{d x} (5 + cot^{2} (x))

Apply the chain rule:

\frac{1}{2 5 + cot ^{2} ( x )} \frac{d}{d x} (5 + cot^{2} (x))

= \frac{1}{2 5 + cot ^{2} ( x )} \frac{d}{d x} (5 + cot^{2} (x))

\frac{d}{d x} (5 + cot^{2} (x)) = - 2 csc^{2} (x) cot (x)

= \frac{1}{2 5 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x))

Simplify

\frac{1}{2 5 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x)) : - \frac{csc ^{2} ( x ) cot ( x )}{5 + cot ^{2} ( x )}

= - \frac{csc ^{2} ( x ) cot ( x )}{5 + cot ^{2} ( x )}

\int d x d x

\int_{0}^{2} π (4 - x^{2})^{2} d x

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

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

n = 1 \sum \infty 8 (- 1)^{n} n x^{n}

What is the derivative of sqrt(5+cot^2(x)) ?
The derivative of sqrt(5+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(5+cot^2(x)))
What is the first derivative of sqrt(5+cot^2(x)) ?
The first derivative of sqrt(5+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(5+cot^2(x)))