The Derivative of Cot(x): Step-by-Step Calculation and Result

(d/dx) cot(x)

To find the derivative of cot(x), we can start by expressing cot(x) in terms of sine and cosine:

cot(x) = cos(x) / sin(x)

Now, let’s find the derivative using the quotient rule:

(d/dx) [cot(x)] = (d/dx) [cos(x) / sin(x)]

Using the quotient rule, the derivative of the numerator is:

d/dx [cos(x)] = -sin(x)

And the derivative of the denominator is:

d/dx [sin(x)] = cos(x)

Using the quotient rule formula:

(d/dx) [cot(x)] = (cos(x) * (-sin(x)) – sin(x) * (-cos(x))) / (sin(x))^2

Simplifying the numerator:

= (-cos(x)sin(x) + sin(x)cos(x)) / (sin(x))^2

= 0

Hence, the derivative of cot(x) with respect to x is zero

To find the derivative of cot(x), we can start by expressing cot(x) in terms of sine and cosine:

cot(x) = cos(x) / sin(x)

Now, let’s find the derivative using the quotient rule:

(d/dx) [cot(x)] = (d/dx) [cos(x) / sin(x)]

Using the quotient rule, the derivative of the numerator is:

d/dx [cos(x)] = -sin(x)

And the derivative of the denominator is:

d/dx [sin(x)] = cos(x)

Using the quotient rule formula:

(d/dx) [cot(x)] = (cos(x) * (-sin(x)) – sin(x) * (-cos(x))) / (sin(x))^2

Simplifying the numerator:

= (-cos(x)sin(x) + sin(x)cos(x)) / (sin(x))^2

= 0

Hence, the derivative of cot(x) with respect to x is zero.

Therefore, (d/dx) [cot(x)] = 0.

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