What is the derivative of xcot(x) ?

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

What is the first derivative of xcot(x) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = cot (x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot cot (x) + (- csc^{2} (x)) x

Simplify

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

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\frac{d}{d x} (6 tan^{2} (3 x))

\int \frac{6 x ^{2} + x + 7}{( x + 1 ) ( x ^{2} + 1 )} d x

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