Differentiate the function e^2x
Also, state whether it is Increasing or Strictly Increasing and what is the difference.

Dear Student,
Solution)
Let y = e^2x          .....(1)
put t = 2x          .......(2)

from (1), we have
y = e^t
differentiating both sides w.r.t 't'
$\frac{dy}{dt} = e^t$
differentiating (2), w.r.t. 'x', we get
$\frac{dt}{dx}= 2$
$now, \frac{dy}{dx}= \frac{dy}{dt}\times \frac{dt}{dx}= e^t \times 2 = 2 e^{2x}$
Now, let x₁ and x₂ be any two numbers belong to R.
Then, we have,
x₁ < x₂
2x₁ < 2x₂ 
So, 
e^2x₁ < e^2x₂
f(x₁) < f(x₂)
Hence, function is strictly increasing on R.

Regards!