Derivative of csc(x)
To find the derivative of csc(x), we can start by writing csc(x) as 1/sin(x)
To find the derivative of csc(x), we can start by writing csc(x) as 1/sin(x). Then, we can use the quotient rule to differentiate it.
Using the quotient rule, the derivative of csc(x) is given by:
d/dx (csc(x)) = (1 * d/dx(sin(x)) – sin(x) * d/dx(1)) / (sin(x))^2
The derivative of sin(x) is simply cos(x), and the derivative of the constant 1 is 0. So, the equation becomes:
d/dx (csc(x)) = (cos(x) * 1 – sin(x) * 0) / (sin(x))^2
Simplifying further, we get:
d/dx (csc(x)) = cos(x) / (sin(x))^2
Therefore, the derivative of csc(x) is cos(x) divided by the square of sin(x):
d/dx (csc(x)) = cos(x) / (sin(x))^2
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