Derivative of cot x
-csc^2 x
The derivative of cot(x) can be found using the quotient rule of differentiation.
Recall that cot(x) = cos(x)/sin(x).
Now, let’s differentiate both the numerator and the denominator separately:
d/dx [cos x] = -sin x
d/dx [sin x] = cos x
Using the quotient rule, we have
d/dx [cot(x)] = [sin^2(x) – cos^2(x)] / [sin^2(x)]
We can simplify this further using the identity sin^2(x) + cos^2(x) = 1:
d/dx [cot(x)] = -cos^2(x) / sin^2(x)
Therefore, the derivative of cot(x) with respect to x is -cos^2(x) / sin^2(x).
More Answers:
[next_post_link]