Hi all,
I'm trying to keep my brain functioning during these extremely trying times. It's been over 50 years since I had calculus in college. But I've always been fascinated with math and science.
So I decided to delve back into calculus. One of the topics in our text book back then consisted of one paragraph about implicit differentiation. However, the prof spent about a week on the subject. I never really got a good handle on it and wanted to see if I could understand it better and try my hand at solving some problems.
I downloaded some problems from the 'Net and tried solving. I ran into one problem that I tried. I came up with an answer, but decided to use one of the online calculators which also shows the steps to solving. You can find that calculator at https://www.symbolab.com/solver/implicit-derivative-calculator.
The problem is: sin(x/y)=1/2
I was able to understand the steps up to:
The next step is shown as: cos(x/y)(-xy' +y) = 0 citing the Zero Factor Principle: If ab=0 then a=0 or b=0 (or both a=0 and b=0)
I'm just not sure what happened to the y2. Did they multiply both sides by y2?
Once again, for the following step, they cite the Zero Factor Principle. But only show: -xy' + y = 0. So did they assume cos(x/y) was zero? Or did they divide each side by it?
From there they finalize the solution as y' = y/x.
Can anyone clarify the two questions I posed above?
Thanks,
Vic
I'm trying to keep my brain functioning during these extremely trying times. It's been over 50 years since I had calculus in college. But I've always been fascinated with math and science.
So I decided to delve back into calculus. One of the topics in our text book back then consisted of one paragraph about implicit differentiation. However, the prof spent about a week on the subject. I never really got a good handle on it and wanted to see if I could understand it better and try my hand at solving some problems.
I downloaded some problems from the 'Net and tried solving. I ran into one problem that I tried. I came up with an answer, but decided to use one of the online calculators which also shows the steps to solving. You can find that calculator at https://www.symbolab.com/solver/implicit-derivative-calculator.
The problem is: sin(x/y)=1/2
I was able to understand the steps up to:
cos(x/y)(-xy' +y) = 0 |
y2 |
The next step is shown as: cos(x/y)(-xy' +y) = 0 citing the Zero Factor Principle: If ab=0 then a=0 or b=0 (or both a=0 and b=0)
I'm just not sure what happened to the y2. Did they multiply both sides by y2?
Once again, for the following step, they cite the Zero Factor Principle. But only show: -xy' + y = 0. So did they assume cos(x/y) was zero? Or did they divide each side by it?
From there they finalize the solution as y' = y/x.
Can anyone clarify the two questions I posed above?
Thanks,
Vic