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# differentiate 2^(x^2) Tweet

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1. differentiate 2^(x^2)
I know if y=a^x dy/dx= (a^x)lna

So for 2^(x^2) would the right answer to this be 2^(x^2)ln2 ?
2. Re: differentiate 2^(x^2)
The easiest way to think about this is to first rewrite x^(x^2) as e^(kx^2). Then simply it would be 2kxe^(kx^2)
3. Re: differentiate 2^(x^2)
(Original post by anonstudent1)
I know if y=a^x dy/dx= (a^x)lna

So for 2^(x^2) would the right answer to this be 2^(x^2)ln2 ?
No.

Example:

Take the natural log of both sides

Now use implicit differentiation,

4. Re: differentiate 2^(x^2)
write it as

then differentiate using chain and product rules
5. Re: differentiate 2^(x^2)
http://www.wolframalpha.com/input/?i...%5E%28x%5E2%29

6. Re: differentiate 2^(x^2)
Let y= 2^(x^2)

Take ln of both sides.
7. Re: differentiate 2^(x^2)
(Original post by Раскольников)
http://www.wolframalpha.com/input/?i...%5E%28x%5E2%29

8. Re: differentiate 2^(x^2)
(Original post by raheem94)
No.

Example:

Take the natural log of both sides

Now use implicit differentiation,

Thank you!
9. Re: differentiate 2^(x^2)
(Original post by raheem94)
No.

Example:

Take the natural log of both sides

Now use implicit differentiation,

Apparently the answer is 3^(x^2)xln9 according to this site http://www.wolframalpha.com/input/?i...%5E%28x%5E2%29
10. Re: differentiate 2^(x^2)
(Original post by anonstudent1)
Apparently the answer is 3^(x^2)xln9 according to this site http://www.wolframalpha.com/input/?i...%5E%28x%5E2%29
Both are correct.

11. Re: differentiate 2^(x^2)
y=2^(x^2)
lny=x^2 ln2
1/y dy/dx=2x ln 2
dy/dx=2^(x^2) 2x ln2

But the answer is 2^(x^(2+1)) x ln2

Can anyone tell me how I get from one to the other, or if my answer is wrong?
12. Re: differentiate 2^(x^2)
(Original post by anonstudent1)
y=2^(x^2)
lny=x^2 ln2
1/y dy/dx=2x ln 2
dy/dx=2^(x^2) 2x ln2

But the answer is 2^(x^(2+1)) x ln2

Can anyone tell me how I get from one to the other, or if my answer is wrong?

You have got
13. Re: differentiate 2^(x^2)
(Original post by raheem94)

You have got
Yh i see. Thank you, you have been very helpful!