What is the derivative of sqrt(9+cot^2(x)) ?

The derivative of sqrt(9+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(9+cot^2(x)))

What is the first derivative of sqrt(9+cot^2(x)) ?

The first derivative of sqrt(9+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(9+cot^2(x)))

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derivative of

9 + cot^{2} (x)

- \frac{csc ^{2} ( x ) cot ( x )}{9 + cot ^{2} ( x )}

Solution steps

\frac{d}{d x} (9 + cot^{2} (x))

Apply the chain rule:

\frac{1}{2 9 + cot ^{2} ( x )} \frac{d}{d x} (9 + cot^{2} (x))

= \frac{1}{2 9 + cot ^{2} ( x )} \frac{d}{d x} (9 + cot^{2} (x))

\frac{d}{d x} (9 + cot^{2} (x)) = - 2 csc^{2} (x) cot (x)

= \frac{1}{2 9 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x))

Simplify

\frac{1}{2 9 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x)) : - \frac{csc ^{2} ( x ) cot ( x )}{9 + cot ^{2} ( x )}

= - \frac{csc ^{2} ( x ) cot ( x )}{9 + cot ^{2} ( x )}

x^{2} (1 - 2 x)

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

n = 0 \sum \infty \frac{1}{1.0 1 ^{n}}

\int_{1}^{\infty} x e^{- 8 x} d x

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

What is the derivative of sqrt(9+cot^2(x)) ?
The derivative of sqrt(9+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(9+cot^2(x)))
What is the first derivative of sqrt(9+cot^2(x)) ?
The first derivative of sqrt(9+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(9+cot^2(x)))