Question

find the derivative of x²-cosx / sin x

please answer...​

Answer 1

x²-cosx/sinx

2x+sinx/ cosx

Answer 2

dy/dx  = (1 - x²Cosx + 2xSinx)/Sin²x if y  = (x²-cosx) / sin x

Step-by-step explanation:

y  = (x²-cosx) / sin x

dy/dx  = (x²-cosx)( -1/Sin²x)Cosx   + (2x - (-Sinx))/Sinx

=> dy/dx  = (x²Cosx-cos²x)( -1/Sin²x)   + (2x + Sinx)/Sinx

=> dy/dx  = (cos²x - x²Cosx)/Sin²x   + (2x + Sinx)/Sinx

=> dy/dx  = ((cos²x - x²Cosx)  + (2xSinx + Sin²x))/Sin²x

=> dy/dx  = (cos²x - x²Cosx + 2xSinx + Sin²x)/Sin²x

=> dy/dx  = (1 - x²Cosx + 2xSinx)/Sin²x

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