What is the derivative of csc^2(xcot(x)) ?

The derivative of csc^2(xcot(x)) is -2csc^2(x)cot^2(x)-csc^4(x)

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

The first derivative of csc^2(xcot(x)) is -2csc^2(x)cot^2(x)-csc^4(x)

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

- 2 csc^{2} (x) cot^{2} (x) - csc^{4} (x)

Solution steps

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

Apply the Product Rule:

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

f = csc^{2} (x), g = cot (x)

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

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

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

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

Simplify

(- 2 csc^{2} (x) cot (x)) cot (x) + (- csc^{2} (x)) csc^{2} (x) : - 2 csc^{2} (x) cot^{2} (x) - csc^{4} (x)

= - 2 csc^{2} (x) cot^{2} (x) - csc^{4} (x)

What is the derivative of csc^2(xcot(x)) ?
The derivative of csc^2(xcot(x)) is -2csc^2(x)cot^2(x)-csc^4(x)
What is the first derivative of csc^2(xcot(x)) ?
The first derivative of csc^2(xcot(x)) is -2csc^2(x)cot^2(x)-csc^4(x)