I need to find the derivative of sin^5(cos(6x))
It is a homework problem, but I am really just wanting someone the order of how I should work this problem.
I need to find the derivative of sin^5(cos(6x))
It is a homework problem, but I am really just wanting someone the order of how I should work this problem.
I cba to do this myself, so here's a nice page for you:
http://www.wolframalpha.com/input/?i...cos%286x%29%29
It should show the solution as well.
...Isn't that what they're meant to teach you and what you listen to in class? And take notes?
guess i was wrong :P heheh
I know right that was what I thought as well not here at my school they don't in most classes they don't even use text books so we can use the text to see how things are done they post some half ass notes they use where they don't show the work used to solve a problem they just show the answer and thats exactly what they do in class as well using the same examples.
Lol at that program. I was about to come in here and do a big explanation.
Yeah, do the multiplication derivative rule.
Chain rule is your friend!
Had trouble understanding but the gist is you don't actually get taught? That's pretty bad. I did this on a course a couple years ago and if you didn't understand the admittedly rushed and brief in lesson content you could get support sessions with the teacher outside of class time where you were both free (usually lunch times and such), and we had a book for reference which did have everything in it if you needed to cover something. Teachers also printed off their presentations and encouraged you to take notes.
You have to do Chain rule a few times. Chain rule: I'O'(I), where I is the inside function and O is the outside function. But you have multiple functions.
Going from furthest out to furthest in: x^5 ; sin(x) ; cos(x) ; 6x
5(sin(cos(6x))^4*Dx(sin(cos(6x))
=5(sin(cos(6x))^4*cos(cos(6x))*Dx(cos(6x))
=5(sin(cos(6x))^4*cos(cos(6x))*-sin(6x)*Dx(6x)
=5(sin(cos(6x))^4*cos(cos(6x))*-sin(6x)*6
Bring all coeffiecients to the front:
=-30[sin(cos(6x))^4*cos(cos(6x))*sin(6x)]
EDIT: Woohoo someone posted WolframAlpha doing the same thing
Damn, beat me to it.
Anyways, like everyone said, it's all chain rule. The trick is to figure out how many times you need to apply it.
You need to apply it once for the power outside the original sin function, once for the actual sin function, once for the cos function inside the sin function, and then finally you need to find the derivative of 6x inside last cos function.
It's basically a problem testing to see if you understand chain rule.
Just because a teacher teaches it once doesn't mean everyone understood. On a good day, I teach by a 80/20 rule. If 80% of what I taught was absorbed, then it's successful. The other 20% need to be retaught, or taught in a different way for them to be a success. Every student CAN learn. It's a teacher's job to find which way speaks to which student. Sadly, though, some students are simply to lazy and refuse to do the work -- making it appear they didn't learn the material.
For some students simply "listening" isn't enough. Some have to work through it a few times, others have to try it from another approach. This is especially important in math. I didn't understand most any math I had in grade school. I didn't get it until I took the general ed math class in college when I had a prof who gave us links to websites that would explain 10 different ways to do different equations so that we could find what works best for us.
"Do not only practice your art, but force yourself into its secrets, for it and knowledge can raise men to the divine." -- Ludwig Van Beethoven