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# differentiate 2^x Watch

1. how would you differentiate 2^x
2. 2^x = e^xln2
3. (Original post by uxa595)
how would you differentiate 2^x
Remember differentiating, , gives,
4. (Original post by Coulson72)
2^x = e^xln2
I got this but i don't think it's right

(Original post by raheem94)
Remember differentiating, , gives,
How do you know a^x foes to a^x lna?
5. (Original post by nm786)

No.
6. (Original post by uxa595)
I got this but i don't think it's right

How do you know a^x foes to a^x lna?
Its a formula.

If
Take the natural log of both sides.

Differentiate implicitly,

We know, , hence,

Do you get it?
7. (Original post by uxa595)
I got this but i don't think it's right

How do you know a^x foes to a^x lna?
If y= a^x

ln(y)= xln(a)

1/y(dy/dx)= ln(a)

dy/dx= a^x(ln(a))
8. (Original post by nm786)
is this for c1?
no
If y= a^x

ln(y)= xln(a)

1/y(dy/dx)= ln(a)

dy/dx= a^x(ln(a))
My is better
10. I got this:

y=2^x
therefore
y= e^(xln2)
y= e^x . e^ln2
y= 2e^x

is that right?
11. (Original post by nm786)
is this for c1?
C1? Holy **** I haven't done this for C4.
12. (Original post by uxa595)
I got this:

y=2^x
therefore
y= e^(xln2)
y= e^x . e^ln2
y= 2e^x

is that right?
No,

Example:

This could have directly been found using the formula i gave you.
13. (Original post by raheem94)
Its a formula.

If
Take the natural log of both sides.

Differentiate implicitly,

We know, , hence,

Do you get it?
Or... (if you're not fond of implicit differentiation):

14. (Original post by uxa595)
I got this:

y=2^x
therefore
y= e^(xln2)
y= e^x . e^ln2
y= 2e^x

is that right?
No.

If y= e^(xln2)

dy/dx= ln2*e^(xln2)

And you should remember: e^(xln2)= 2^x.
15. (Original post by notnek)
Or... (if you're not fond of implicit differentiation):

See post#14 in this thread, i know it mate.
16. (Original post by raheem94)
No,

Example:

This could have directly been found using the formula i gave you.
Ahhh right, thanks, i've got it now

I can't remember doing this ever in class
17. (Original post by raheem94)
See post#14 in this thread, i know it mate.
I assumed you knew it. I posted it for the OP.
18. Just tried this myself

Doing it implicitly seems the most straight forward

Updated: May 9, 2012
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