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Popular >

derivative of xcsc(x-cot(x))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

Graph

Popular Examples

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n = 0 \sum \infty \frac{6}{2 ^{n}}

derivative of f(x)=(-6)/x derivative of

f (x) = \frac{- 6}{x}

(\partial)/(\partial x)(-8xy-2x^4-2y^4)

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limit as x approaches 0 of (6^x-5^x)/x

x \to 0 lim (\frac{6 ^{x} - 5 ^{x}}{x})

derivative of f(x)=(x-3)/(x+3)derivative of

f (x) = \frac{x - 3}{x + 3}

Frequently Asked Questions (FAQ)

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