derivative of cscx
To find the derivative of csc(x), we can use the chain rule
To find the derivative of csc(x), we can use the chain rule. The derivative of csc(x) is defined as the derivative of 1/sin(x).
Let’s break it down step by step:
Step 1: Rewrite csc(x) as 1/sin(x).
Step 2: Apply the quotient rule. The quotient rule states that the derivative of f(x)/g(x) is (g(x)f'(x) – f(x)g'(x))/[g(x)]².
In this case, f(x) = 1 and g(x) = sin(x).
Step 3: Find the derivative of f(x), which is f'(x). In this case, f'(x) = 0, because the derivative of a constant is always zero.
Step 4: Find the derivative of g(x), which is g'(x). In this case, g'(x) = cos(x), because the derivative of sin(x) is cos(x).
Now we have all the pieces we need to apply the quotient rule:
(csc(x))’ = [(sin(x) * 0) – (1 * cos(x))] / [sin(x)]^2
= -cos(x) / sin²(x)
Therefore, the derivative of csc(x) is equal to -cos(x) / sin²(x).
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