What is the derivative of cos(xcot(x)) ?

The derivative of cos(xcot(x)) is -cos(x)-cot(x)csc(x)

What is the first derivative of cos(xcot(x)) ?

The first derivative of cos(xcot(x)) is -cos(x)-cot(x)csc(x)

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

- cos (x) - cot (x) csc (x)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

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

Simplify

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

= - cos (x) - cot (x) csc (x)

\int a^{2} - x^{2} d x

e^{- 2 t} cos (4 t)

x = 5 - 5 y^{2}, x = 5 y^{2} - 5

\frac{d}{d x} ((tan (- 1 (7 x))) 2)

\frac{d}{d x} (\frac{x ^{4}}{1 - x ^{3}})

What is the derivative of cos(xcot(x)) ?
The derivative of cos(xcot(x)) is -cos(x)-cot(x)csc(x)
What is the first derivative of cos(xcot(x)) ?
The first derivative of cos(xcot(x)) is -cos(x)-cot(x)csc(x)