Differentiate the function e^2x
Also, state whether it is Increasing or Strictly Increasing and what is the difference.
Dear Student,
Solution)
Let y = e2x .....(1)
put t = 2x .......(2)
from (1), we have
y = et
differentiating both sides w.r.t 't'
differentiating (2), w.r.t. 'x', we get
Now, let x1 and x2 be any two numbers belong to R.
Then, we have,
x1 < x2
2x1 < 2x2
So,
e2x1 < e2x2
f(x1) < f(x2)
Hence, function is strictly increasing on R.
![](https://s3mn.mnimgs.com/img/shared/content_ck_images/ck_61a4a081c8607.jpg)
Regards!
Solution)
Let y = e2x .....(1)
put t = 2x .......(2)
from (1), we have
y = et
differentiating both sides w.r.t 't'
differentiating (2), w.r.t. 'x', we get
Now, let x1 and x2 be any two numbers belong to R.
Then, we have,
x1 < x2
2x1 < 2x2
So,
e2x1 < e2x2
f(x1) < f(x2)
Hence, function is strictly increasing on R.
![](https://s3mn.mnimgs.com/img/shared/content_ck_images/ck_61a4a081c8607.jpg)
Regards!