Q. 135.0( 1 Vote )

Differentiate the following functions with respect to x:


Answer :

Let, y =


We have to find dy/dx


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


u = sin x – x cos x and v = x sin x + cos x


y = u/v


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


By quotient rule, we have –


…equation 1


u = – (x cos x – sin x)



Using algebra of derivatives –




{using product rule}


…equation 2


As, v = x sin x + cos x



Using algebra of derivatives –




{using product rule}


…equation 3


from equation 1, we can find dy/dx



using equation 2 and 3, we get –





Hence,



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