Derivative of csc x
The derivative of the cosecant function (csc x) can be found using the quotient rule
The derivative of the cosecant function (csc x) can be found using the quotient rule.
The quotient rule states that if you have a function of the form f(x) = g(x)/h(x), where g(x) and h(x) are differentiable functions, then the derivative of f(x) is given by f'(x) = (g'(x)h(x) – g(x)h'(x))/[h(x)]^2.
To apply this rule to find the derivative of csc x, we can write it as csc x = 1/sin x. Using the quotient rule, we have:
csc'(x) = [(1)'(sin x) – (1)(sin x)’]/[sin x]^2
= [0 – cos x]/[sin x]^2
= -cos x/[sin x]^2
Therefore, the derivative of csc x is -cos x/[sin x]^2.
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