Question

2x+x²+tanx
let y=2x+x²+tanx
Now, Different w. r. to x
dy/dx=d/dx =(2x+x²+tanx)
d/dx=2+2x¹+sec²x
dy/dx=2+2x+sec²x​

Answer 1

Answer:

Let y = sec^2 x. Let sec x = t.

Then. y = t^2. This implies dy/dt = 2t = 2 sec x

t = sec x implies dt/dx = sec x.tan x.

So. dy/dx = (dy/dt)×(dt/dx)

= 2sec x . sec x. tan x = 2 sec^2 x .tan x.

(OR) by using chain rule we can get the answer directly.

y = sec^2 x. Implies dy/dx = 2sec x.sec x.tan x

2sec^2 x. tan x.