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.
Update on Things
Good day everyone, I hope you are doing well. I am sorry it has been a while, I am participating in my son’s Science Olympiad, it is a lot of fun and time consuming. I wanted to give some insight on the world, they do not teach us about stock, bonds in school. They think…
Plan for 2026
A belated Happy New Year to everyone, I hope the new year is a good one for you. I am thinking I am going to go into a new direction and apply engineering knowledge to companies and see if they are worth investing in. Keep in mind this is an my evaluation based on engineering…
Update
I am almost done with my PHd in mechanical engineering. I just need to get through the audit. Once I am done I will put links to my papers and start analyzing the world Another Update Good day all, I hope you are enjoying the weekend, I am graduating this week with my PHD in…
Site Title 
Leave a comment