What is the derivative of cot(xdx) ?

The derivative of cot(xdx) is d(-xcsc^2(x)+cot(x))

What is the first derivative of cot(xdx) ?

The first derivative of cot(xdx) is d(-xcsc^2(x)+cot(x))

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

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

Solution steps

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

Treat

d

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = cot (x), g = x

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

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

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

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

Simplify

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

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