d/dx csc(x)
To find the derivative of csc(x), we will use the quotient rule
To find the derivative of csc(x), we will use the quotient rule.
The quotient rule states that for a function f(x) = g(x) / h(x), the derivative is given by:
f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2
In this case, g(x) = 1 and h(x) = sin(x).
Let’s find the derivatives of g(x) and h(x):
g'(x) = 0 (the derivative of a constant is zero)
h'(x) = cos(x) (the derivative of sin(x) is cos(x))
Now substituting these values in the quotient rule formula, we get:
f'(x) = (0 * sin(x) – 1 * cos(x)) / (sin(x))^2
= -cos(x) / sin^2(x)
Therefore, the derivative of csc(x) is -cos(x) / sin^2(x).
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