# y=e^x

Watch
#1
so it says "there is going to be a value of a for which the gradient of y=a^x is exactly the sames as a^x. known as e"

that means dy by dx =2e^2x is equal to e^2x which is not equal when a sub in x as 1...

confused
0
1 week ago
#2
(Original post by Jshek)
so it says "there is going to be a value of a for which the gradient of y=a^x is exactly the sames as a^x. known as e"

that means dy by dx =2e^2x is equal to e^2x which is not equal when a sub in x as 1...

confused

Your exponent is 2x, not x.

If you put your function into the form a^x, you have and e^2 does not equal e, and doesn't meet your criterion.
0
#3
(Original post by ghostwalker)
Your exponent is 2x, not x.

If you put your function into the form a^x, you have and e^2 does not equal e, and doesn't meet your criterion.
i dont understand
0
#4
(Original post by Jshek)
i dont understand
it said it should equal in my book
0
1 week ago
#5
(Original post by Jshek)
so it says "there is going to be a value of a for which the gradient of y=a^x is exactly the sames as a^x. known as e"

that means dy by dx =2e^2x is equal to e^2x which is not equal when a sub in x as 1...

confused
As ghostwalker said
e^(2x) = (e^2)^x
Which is not e^x.

Have you done the derivative
d(a^x)/dx = ln(a)a^x
? If so, this equals a^x when ln(a)=1, so a=e. This agrees with your example as ln(e^2)=2.

It may help to post a pic of the page you're confused about so we can see the context.
Last edited by mqb2766; 1 week ago
0
#6

So I read 14.2 and it says there's going to be a valid of a where gradient function is exactly same as original function

So I look at example 3a.... e^4x and its gradient function 4e^4x. I then sub in x=1 but this contradicts the sentence above as they do not equal
0
#7
(Original post by Jshek)

So I read 14.2 and it says there's going to be a valid of a where gradient function is exactly same as original function

So I look at example 3a.... e^4x and its gradient function 4e^4x. I then sub in x=1 but this contradicts the sentence above as they do not equal
Value instead of valid i meant

Clearer image
0
1 week ago
#8
(Original post by Jshek)

So I read 14.2 and it says there's going to be a valid of a where gradient function is exactly same as original function

So I look at example 3a.... e^4x and its gradient function 4e^4x. I then sub in x=1 but this contradicts the sentence above as they do not equal
To try and simplify things a bit. Imagine e=3 (engineering approximation of the true value 2.718...).
Then
e^(4x) = (e^4)^x ~ 81^x
This is not e^x ~ 3^x. Just plug in x=1,2,3,... Multiplying the exponent "x" by a constant changes the base "e" so the conclusion about the derivative is no longer true.
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

What I expected (83)
25.08%
Better than expected (71)
21.45%
Worse than expected (177)
53.47%