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Popular >

derivative of sqrt(1+cot^2(x))

Solution

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

Solution

- csc (x) cot (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - csc (x) cot (x)

Popular Examples

integral of (x^2+8)e^{-x}

\int (x^{2} + 8) e^{- x} d x

limit as x approaches infinity of 6/x

x \to \infty lim (\frac{6}{x})

tangent of y=sqrt(3x+1),(5,16)tangent of

y = 3 x + 1, (5, 16)

derivative of (c^2-x^2)/(c^2+x^2)derivative of

\frac{c ^{2} - x ^{2}}{c ^{2} + x ^{2}}

sum from n=0 to infinity of n+1

n = 0 \sum \infty n + 1

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(1+cot^2(x)) ?
The derivative of sqrt(1+cot^2(x)) is -csc(x)cot(x)
What is the first derivative of sqrt(1+cot^2(x)) ?
The first derivative of sqrt(1+cot^2(x)) is -csc(x)cot(x)