Anyone in for a little Math?

[limacon]

I got a High School/College Math question that needs an answer. First and foremost, this is NOT my homework!

My friend asked me for some help but I've got already passed this part of Math so I kinda forgotten the right way to do it.

I am very willing to give +rep to anyone who could answer this right. Thank you.

Q: Find the derivative (dy/dx) of y=x^(3^x)

[tealeaf]

solving derivatives step-by-step
WebMath - Solve Your Math Problem

Plug it into there ;D

[limacon]

Aw.. It still can't solve it because it's kinda different. I mean you are raising x to a constant exponent which is raised to a variable.


Thanks though!

[GotRice[?]]

That's the first time I've encountered that sort of derivative. What year of studies you in? Uni level right?

[popirate]

You're probably in AP, huh?
I'm still in Pre-Calculas, ugh.

[illidari]

/shudder calculus

Wish I could help but my brain is on summer vacation.

[Deathblck]

dur a huh um fu loo....im so confused...i would never pass

[Air]

Originally Posted by limacon

I got a High School/College Math question that needs an answer. First and foremost, this is NOT my homework!

My friend asked me for some help but I've got already passed this part of Math so I kinda forgotten the right way to do it.

I am very willing to give +rep to anyone who could answer this right. Thank you.

Q: Find the derivative (dy/dx) of y=x^(3^x)

y=x^(3^x)

Take the natural logarithm of both sides:

ln(y) = (3^x)(ln(x))

Now differentiate both sides with respect to 'x'. Left hand side is done with implicit differentiation and right hand side is done with product and chain rule:

(1/y)(dy/dx) = (3^x)/x + (3^x)(ln(3))(ln(x))

Multiply both sides to get by 'y' to leave 'dy/dx' on it's own:

dy/dx = y[(3^x)/x + (3^x)(ln(3))(ln(x))]

As 'y=x^(3^x)', replace this so that the whole expression is in terms of 'x':

dy/dx = x^(3^x)[(3^x)/x + (3^x)(ln(3))(ln(x))]