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Popular >

derivative of csc(xcot(x))

Solution

\frac{d}{d x} (csc (x) cot (x))

Solution

csc (x) - 2 csc^{3} (x)

Solution steps

\frac{d}{d x} (csc (x) cot (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = csc (x), g = cot (x)

= \frac{d}{d x} (csc (x)) cot (x) + \frac{d}{d x} (cot (x)) csc (x)

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

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

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

Simplify

(- cot (x) csc (x)) cot (x) + (- csc^{2} (x)) csc (x) : csc (x) - 2 csc^{3} (x)

= csc (x) - 2 csc^{3} (x)

Popular Examples

f(t)=80e^{-t/(10)}-40t

f (t) = 80 e^{- \frac{t}{10}} - 40 t

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\frac{x}{x - 7}

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\int (sin^{2} (x) cos (x)) d x

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x^{2}

area f(x)=-x^2+2,g(x)=-x-4 area

f (x) = - x^{2} + 2, g (x) = - x - 4

Frequently Asked Questions (FAQ)

What is the derivative of csc(xcot(x)) ?
The derivative of csc(xcot(x)) is csc(x)-2csc^3(x)
What is the first derivative of csc(xcot(x)) ?
The first derivative of csc(xcot(x)) is csc(x)-2csc^3(x)