Derivative of csc x
How to find the derivative of the given function by using the derivative of csc x: formula, 1 example, and its solution.
The derivative of csc x, [csc x]',
is -csc x cot x.
Exampley = csc (1 - x2), y' = ?
y = csc (1 - x2)
is a composite function of
y = csc (whole) and (whole) = 1 - x2.
So the derivative of the composite function is,
the derivative of the outer function csc (1 - x2), -csc (1 - x2) cot (1 - x2)
the derivative of the inner function 1 - x2, -2x1.
-(-2x1) = 2x
So the right side is
2x csc (1 - x2) cot (1 - x2).
2x csc (1 - x2) cot (1 - x2)
is the derivative of csc (1 - x2).