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implicit differentiation question, help watch

1. find the equation of the tangent to the curve y=2^x + 2^-x at the point (2, 4 1/4).

need help, both me an brother are getting the wrong answer

thanks, xxx
2. Do you know how to differentiate ax functions?

If not think about y = ax => ln y = ln (ax) = x ln a (so now ln a is a constant)
3. i think i do to some extent, i got as far as

dy/dx= 2^x(ln2) + 2^-x(ln2)
substitute 2 into x

= 4ln2 + 1/4ln2
=ln2^4 + ln2^1/4

then i get stuck
4. 4 ln 2 - (1/4) ln 2 = (15/4) ln 2

this is the gradient at the point (2, 17/4)
5. hi...do u happen 2 have the answer to this question...i attempted it...but dont want 2 post answer for it jus to be wrong...if u post the answer i can see whether i got the right thing then post the solution??
6. yeah sure, the answer is 4y= 15ln2(x-2) + 17

xx
7. [mod edit: can you not post full solutions on the forum]
8. Please do not post full solutions
9. differentiation wise, I managed to solve using the relationship:
2^x=(e^(ln2))^x=e^(xln2)
and similarly for 2^(-x) =>e^(-xln2)
then differentiated each term with the chain rule - thus avoiding implicit differentiation :-)
10. you don't take logs of both sides - do each term separately

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Updated: January 24, 2010
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