Question:
Find the derivative of the following functions: (Sinx+Cosx) /(Sinx-Cosx)
Answer:
Let y= (Sinx+Cosx) /(Sinx-Cosx)
dy/dx = [(Sinx-Cosx) *(Cosx - Sinx) - (Sinx+Cosx)*(Cosx+Sinx)]/(Sinx-Cosx)2
= [-(Sinx-Cosx)2 -(Sinx+Cosx)2 ]/(Sinx-Cosx)2
= -[(Sinx-Cosx)2 +(Sinx+Cosx)2 ]/(Sinx-Cosx)2
= -[Sin2 x+Cos2 x-2*Sinx*Cosx + Sin2 x+Cos2 x+2*Sinx*Cosx]/(Sinx-Cosx)2 (SinceSin2 x+Cos2 x = 1)
= -(1+1)/(Sinx-Cosx)2
=- 2/(Sinx-Cosx)2
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