Derivative cscx
The derivative of the csc(x) function can be found using the quotient rule
The derivative of the csc(x) function can be found using the quotient rule. The csc(x) function is the reciprocal of the sine function, which means csc(x) = 1/sin(x).
To find the derivative, we need to differentiate the numerator and denominator of this quotient separately, and then apply the quotient rule.
Let’s start with the numerator, which is the constant 1. The derivative of a constant is always zero, so the numerator differentiates to 0.
Next, let’s differentiate the denominator, sin(x). The derivative of sin(x) is cos(x), as given by the basic differentiation rule of trigonometric functions.
Now, applying the quotient rule, we plug in the differentiated values into the formula:
(denominator * derivative of numerator – numerator * derivative of denominator) / (denominator)^2
Since the numerator (1) differentiates to 0, we can simplify the formula:
(0 * denominator – 1 * cos(x)) / (denominator)^2
– cos(x) / (sin(x))^2
So, the derivative of csc(x) is -cos(x) / (sin(x))^2.
This derivative formula tells us how the rate of change of the csc(x) function varies with respect to the variable x at any given point.
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