d/dx(cscx)
cscxcotx
To find the derivative of csc(x), we’ll need to use the quotient rule along with the knowledge of derivative of sine function.
We know that csc(x) is equal to 1/sin(x). We can rewrite this as follows:
csc(x) = (sin(x))^(-1)
Using the power rule for differentiation and chain rule, we can find the derivative:
d/dx[csc(x)] = d/dx[(sin(x))^(-1)]
= -1*(sin(x))^(-2)*cos(x)
= -cos(x)*(sin(x))^(-2)
Therefore, the derivative of csc(x) is -cos(x)*(sin(x))^(-2), or alternatively we can write it as -cot(x)csc(x).
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