derivative of cscx
derivative of csc(x) is -cos(x) / sin(x)^2.
The derivative of csc(x) can be found by using the quotient rule and the chain rule. We know that csc(x) is the reciprocal of sin(x), so we can rewrite the function as:
csc(x) = 1 / sin(x)
Next, we can use the quotient rule, which states that d/dx (f(x) / g(x)) = [g(x) * f'(x) – f(x) * g'(x)] / g(x)^2. Let’s apply this rule to our function:
d/dx csc(x) = d/dx (1 / sin(x))
= [sin(x) * 0 – 1 * cos(x)] / sin(x)^2 (applying the quotient rule and using the derivative of sin(x) = cos(x))
= -cos(x) / sin(x)^2
Therefore, the derivative of csc(x) is -cos(x) / sin(x)^2.
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