The chain rule is use to work with an intermittent variable or transform a function into another variable and it also helps out with other functions like y=sin(2x).
So if we have y=sin(x) we can show that the derivative is dy/dx= cos(x) but what do we do when have a constant like y=sin(a*x)
Below is the chain rule, where y is a function of x, but we can rewrite y in terms of u and u in terms of x .
So for the case y=sin(a*x) we will rewrite as y=sin(u), u=a*x
dy/du=cos(u); du/dx=a; and when we combine we get
dy/dx=cos(u)*a but u=a*x; so
dy/dx=a *cos(a*x)
I am going to try to do videos, but I need to get the kids to go to bed.
Thank you for your time and Happy New Year.
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