1.

Differentiate(i) y = tan 3x(ii) y = cos (tan x)

Answer»

(i) y = tan 3x 

Put u = 3x

du/dx = 3

Now y = tan u

du/dx = sec2 u

So dy/dx = (dy/du) x (du/dx) = sec2 u (3)

= 3 sec2 3x

(ii) y = cos (tan x)

Put u = tan x 

du/dx = sec2 x 

Now y = cos u ⇒ du/dx = – sin u 

Now dy/dx = (dy/du) x (du/dx) 

= (-sin u) (sec2 x) 

= – sec2 (sin (tan x))


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