To determine

To evaluate: The derivative dydx

Answer

The value of derivative of y is dydx=cscx

Explanation

Given that: y=ln(cscx−cotx)

Formula used:

1. Chain rule: dfdx=dfdududx

Calculation

To calculate dydx  we apply chain rule. For applying chain rule, let u=cscx−cotx. Then, y=lnu

Differentiate it with respect x, we get

dydx=ddx(lnu)=ddu(lnu)dudx                                            (By chain rule)=1uddx(u)=1cscx−cotxddx(cscx−cotx)               (By replacing value u=cscx−cotx)=1cscx−cotx(ddxcsc−ddxcotx)=1cscx−cotx(−cscxcotx−(−csc2x))=cscx(−cot+cscx)cscx−cotx=cscxConclusion: Thus, the derivative of y is dydx=cscx.