How To Find The Derivative Of Cosecant Function Using Quotient Rule Of Differentiation

d/dx csc(x)

-csc(x)cot(x)

We can start this problem by using the quotient rule of differentiation since the cosecant function could be expressed as 1/sin(x). So, applying the quotient rule,

d/dx (csc(x)) = d/dx (1/sin(x))

= -1/sin^2(x) * d/dx(sin(x))

We know that the derivative of sin(x) with respect to x is cos(x), so

d/dx (csc(x)) = -1/sin^2(x) * cos(x)

Therefore, the derivative of the cosecant function is:

d/dx (csc(x)) = -cot(x)csc(x)

where cot(x) is the cotangent function and it is equal to cos(x)/sin(x).

So, the final answer is:

d/dx (csc(x)) = -cos(x)/(sin^2(x))

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