What is the derivative of y=csc(x)cot(x) ?

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

What is the first derivative of y=csc(x)cot(x) ?

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

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derivative

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)

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