Differentiate the following functions with respect to x:

Let, y = { cos π/4 = 1/√2 }


We have to find dy/dx


As we can observe that y is a product of two functions say u and v where,


u = x2 and v = cosec x


y = (1/√2) uv


As we know that to find the derivative of product of two function we apply product rule of differentiation.


By product rule, we have –


…equation 1


As, u = x2


…equation 2 { }


As, v = cosec x



…equation 3 { }


from equation 1, we can find dy/dx



{using equation 2 & 3}


Hence,



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