Question:
dy/dt if y=Xtanx/secx tanx
Answer:
Given y = (x*tan x)/(sec x + tan x)
=> y = (x * sin x/cos x)/(1/cos x + sin x/cos x)
=> y = (x * sin x)/(1 + sin x)
Now, dy/dx = {(1 + sin x) * d(x * sin x)/dx - (x * sin x) * d(1 + sin x)/dx}/(1 + sin x)2
=> dy/dx = {(1 + sin x) * (x*cos x + sin x) - (x * sin x) * cos x}/(1 + sin x)2
=> dy/dx = {x*cos x + sin x + x*cos x*sin x + sin2 x - x * sin x * cos x}/(1 + sin x)2
=> dy/dx = {x*cos x + sin x + sin2 x}/(1 + sin x)2
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