What is the derivative of y=sqrt(11+cot^2(x)) ?

The derivative of y=sqrt(11+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(11+cot^2(x)))

What is the first derivative of y=sqrt(11+cot^2(x)) ?

The first derivative of y=sqrt(11+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(11+cot^2(x)))

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derivative of

y = 11 + cot^{2} (x)

- \frac{csc ^{2} ( x ) cot ( x )}{11 + cot ^{2} ( x )}

Solution steps

\frac{d}{d x} (11 + cot^{2} (x))

Apply the chain rule:

\frac{1}{2 11 + cot ^{2} ( x )} \frac{d}{d x} (11 + cot^{2} (x))

= \frac{1}{2 11 + cot ^{2} ( x )} \frac{d}{d x} (11 + cot^{2} (x))

\frac{d}{d x} (11 + cot^{2} (x)) = - 2 csc^{2} (x) cot (x)

= \frac{1}{2 11 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x))

Simplify

\frac{1}{2 11 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x)) : - \frac{csc ^{2} ( x ) cot ( x )}{11 + cot ^{2} ( x )}

= - \frac{csc ^{2} ( x ) cot ( x )}{11 + cot ^{2} ( x )}

\frac{d}{d x} (I n (x))

\int sin^{4} (θ) cos^{5} (θ) d θ

- x, \frac{1}{2} x - \frac{3}{2}, - 1, 3

\frac{d}{d t} (1 + t^{2})

x \to - 3 - lim (- x^{2} - x + 4)

What is the derivative of y=sqrt(11+cot^2(x)) ?
The derivative of y=sqrt(11+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(11+cot^2(x)))
What is the first derivative of y=sqrt(11+cot^2(x)) ?
The first derivative of y=sqrt(11+cot^2(x)) is -(csc^2(x)cot(x))/(sqrt(11+cot^2(x)))