What is the derivative of cot^2(xcsc(x)) ?

The derivative of cot^2(xcsc(x)) is -2csc^3(x)cot(x)-cot^3(x)csc(x)

What is the first derivative of cot^2(xcsc(x)) ?

The first derivative of cot^2(xcsc(x)) is -2csc^3(x)cot(x)-cot^3(x)csc(x)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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