Derivative of cot x
The derivative of cot x can be found by using the quotient rule
The derivative of cot x can be found by using the quotient rule. Let’s first write cot x in terms of sin x and cos x.
cot x = cos x / sin x
Applying the quotient rule, we have:
(d/dx) [cot x] = [(d/dx) (cos x)(sin x) – (cos x)(d/dx) (sin x)] / (sin x)^2
Next, let’s find the derivative of sin x and cos x:
(d/dx) (sin x) = cos x
(d/dx) (cos x) = -sin x
Substituting these values back into the quotient rule equation, we get:
= [(cos x)(cos x) – (cos x)(-sin x)] / (sin x)^2
= [(cos^2 x + sin x cos x)] / (sin x)^2
= [(cos^2 x + sin x cos x)] / sin^2 x
= cos x / sin x + cos x / sin^2 x
= cot x + cos x / sin^2 x
Therefore, the derivative of cot x is cot x + cos x / sin^2 x.
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