d/dx cot(x)
To find the derivative of cot(x) with respect to x, we will use the quotient rule
To find the derivative of cot(x) with respect to x, we will use the quotient rule.
The cotangent function can be written as cot(x) = cos(x)/sin(x).
Let’s differentiate the numerator and denominator separately:
Numerator:
d/dx(cos(x)) = -sin(x) (by applying the chain rule)
Denominator:
d/dx(sin(x)) = cos(x) (by applying the chain rule)
Now, applying the quotient rule:
d/dx(cot(x)) = (denominator * numerator’ – numerator * denominator’) / (denominator^2)
= (cos(x) * (-sin(x)) – (-sin(x)) * cos(x)) / sin(x)^2
= (-cos(x)sin(x) + sin(x)cos(x)) / sin(x)^2
= 0 / sin(x)^2
= 0
Therefore, the derivative of cot(x) with respect to x is 0.
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