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

Dear Student,
Let y = e2x          .....(1)
put t = 2x          .......(2)

from (1), we have
y = et
differentiating both sides w.r.t 't'
dydt = et
differentiating (2), w.r.t. 'x', we get
dtdx= 2
now, dydx= dydt×dtdx= et × 2 = 2 e2x
Now, let xand xbe any two numbers belong to R.
Then, we have,
x< x2
2x< 2x
e2x< e2x2
f(x1) < f(x2)
Hence, function is strictly increasing on R.


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