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 = x tan x and v = sec x + tan 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


As, u = x tan x


u is the product of two function x and tan x, so we will be applying product rule of differentiation –



[using product rule]


, So we get –


…equation 2


As, v = sec x + tan x


& , so we get –


…equation 3


from equation 1, we can find dy/dx



using equation 2 and 3, we get –






Hence,



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