Find y' given the following function:
So far, I have:
Having trouble combining the y's.
Another one I am stuck on is:
I am not positive if it is okay to bring the cos(15x) into the front of the ln in this case?
Thanks for any help!
Well, for any positive a and any real x, the identity a^x = e^(x*ln(a)) is pretty easy to check.
In our case it perhaps makes it easier to differentiate since the derivative of the exponential function is very easy......and still you need a logarithmic differentiation.
You can try to differentiate directly though, but I'm afraid it's gonna get nasty. I, for one, would never, ever do it directly.
[e^(cos15x lnx)]' = [cos15x lnx]'*e^(cos15x lnx) =
[-15sin15x lnx + cos15x/x]*ln(x)^(cox15x) , and we're done.
I can't understand from where did you bring that -1 in the power of e. Apparently you confused something here and tried to derivate something as a polynomial : (x^n)' = n x^(n-1)...or stuff.
I am graphing the derivative of the original function and the solution you just posted for the derivative. They don't match up.
On top of that, I'm entering that in for the derivative (it's an online assignment) and it's still getting marked as incorrect..I've checked it several times to make sure I'm not making mistakes typing it in.