150000(0.00625/1-(0.99378)^12t)
solve for dt/dx

x = 150000(\frac{0.00625}{1-(0.99378)^{12t}})

Well, just change the way it looks:

x = \frac{937.5}{1-(0.99378)^{12t}}

x = (937.5)(1-0.99378)^{12t})^{-1}

Now, it's just like:

x = 2(1-3^{2t})^{-1}

\frac{dx}{dt} = -2(1-3^{2t})^{-2} \times -2(3^{2t})

Then you simplify.

Post your answer, to see what you got as answer.

EDIT: Thanks KISS, I forgot that the whole thing was inversed. :o

Jerry, exponentiation takes precidence, thus it's (#^12)*t as it's written.

Wolfram alpha confirms: http://www.wolframalpha.com/input/?i=x%3D15000%280.00625%2F1-%280.99378%29^12t%29

Doing the derivative using #^(12t) and not (#^12)*t one gets:

http://www.wolframalpha.com/input/?i=+derivative+x%3D15000%280.00625%2F1-%280.99378%29^%2812t%29%29

Ohh, shoo, I was in a rush...

I'm editing my previous post.

PS: Although, I just noticed it says dt/dx which is unusual.

Lots of things don't seem quite right. Either that, it's a problem to separate the men from the boys.

When I was in class, exams had typically 4 problems. 2 were easy and anyone could get it right. One was moderately difficult, but nothing tricky. This would be the 4th problem.

Kind of easy: 2 probs right, did your HW = C
You can think ahead - you got a B
Your smart - A

I have to learn to write in that weird script.

Oh ho, I didn't notice that either... well, if that is so, the derivative only has to be inversed.

Well nowadays, getting the tricky one isn't that difficult. Once one has done the problem once, he/she''ll be able to do it good next time, that can be in exams.