It looks like you've forgot about the power on the sin(4x)
Using the chain rule:
Spoiler:
Hi, I am trying to use chain rule to find the derivative of this but I can't seem to get the right answer. I used the same method with other questions and I get the right answer but not with this one here. I took a screenshot of what I did....I'm not sure what I'm doing wrong though. Thanks!
Hey thanks. I don't quite understand this whole "dy/dx = du/dx X dv/du X dy/dv" stuff I have this form in my textbook too but I'm not sure what it means or how their solving it...I know about Dx and F'(x). DxF(x) means that Dx is operating on F(x) to get another function F'(x)...
Could you please explain that?
You can think of it like a fraction:
Consider: - can you see that 2 and 3 will cancel because they are on the top and the bottom which leaves
It is much the same thing but although technically you don't cancel them but it works in the same way (confusing yes but you can treat as a fraction).
In what I did before
note that and will cancel.
Of course since that sum gives an answer of terms of u and v you need to go back to the original substitutions which I made at the top of my post to get in terms of x.
As for DxF(x) I have no idea how that notation works
I'm still not sure how you solved it....sorry I'm really bad at calculus :| What I don't understand is that the chain rule is F'(x) = F'(g(x)) X g'(x) which only has two functions F(x) and g(x)...but you have y (or F(x) i think), u and v....could you possibly solve it in a different way? I really don't like this dy/dx notation and even before starting the chain rule I always (and so did my teacher) used either F'(x) or Dx..
thanks again for helping..
Since we need to use the chain rule three times I shall use f(x), g(x) and h(x)
If and
Hence: and
I cannot use the Dx notation unless you explain it to me because I have no idea what it means
edit: wolfram uses much the same method: WolframAlpha
If you were to evaluate at , how would you do it?
One would first multiply ; then what.
Find the sine of that number, RIGHT?
Then take that result and raise it to the third power.
So to find the derivative of we take a chain of derivatives in exactly the reverse order:
the derivative of the third power; the derivative of sine; the derivative of 4x.
. The derivative of sine is cosine.