The Derivative Of The Reciprocal Trigonometric Function Csc(X) For Better Calculus Performance

derv csc (x)

-(csc(x)cot(x))

The expression derv csc(x) is not clear, as derv is not a standard mathematical notation. However, assuming that you meant to write derivative of csc(x), I will provide an explanation.

The function csc(x) is the reciprocal of the sine function. It is defined as:

csc(x) = 1 / sin(x)

To find the derivative of csc(x), we can use the quotient rule of differentiation. Let’s define the function f(x) = 1 and g(x) = sin(x). Then, we can write csc(x) as:

csc(x) = f(x) / g(x)

Using the quotient rule, the derivative of csc(x) is:

csc'(x) = [f'(x)g(x) – f(x)g'(x)] / [g(x)]^2

Since f(x) = 1, we have f'(x) = 0. The derivative of g(x) is cos(x), so we have:

csc'(x) = [0*cos(x) – 1*cos(x)] / sin^2(x)

Simplifying this expression, we get:

csc'(x) = -cos(x) / sin^2(x)

Therefore, the derivative of csc(x) is equal to negative cosine of x divided by sine squared of x.

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