This week in Calculus AB, things got a little harder. I do not understand how to solve a problem with many parts. I am slowly catching on, but still confused. The thing I understand most in Calculus this week was the arc trig identities.
For example, I understand how to do a problem like arccos (1/x2). First, you must know the formula for arccos, which is (1/ √1-u²) (u’). Take this problem step by step to solve it efficiently. First, find your “u,” which, in this problem, is (1/x²). Now, plug it into the first part of your equation that asks for the “u” to receive the beginning of the equation which should be (1/ (√1-(1/(x²)²). Now you must find u’, or the derivative of u. You can find this by doing the quotient rule, which is: [ (copy the bottom) (derivative of the top) – (copy the top) (derivative of the bottom) ] / (bottom)². The equation should look like ( (x²)(0) – [ (2)(1) ] ) / (x²)² = (-2x)/ (x^4) = (-2) / (x^3). You should use brackets to remind yourself when you are simplifying that you have a negative to distribute. So far, your problem should look like 1/ ( √1- (1/x^4) ) ( (-2) / (x^3) ). The rest of the problem can be solved by algebra to obtain an answer of (2/x^3√1-(1/x^4)). These types of problems are the simplest to solve for me because it only involves plugging in formulas to solve.
If anyone can help me understand order of operations for derivatives it would help me a lot. I’m not sure if you are supposed to take derivatives of everything or if you should work from inside out, then take derivative. I am just very confused on how you should work problems that include more than one rule.
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Mrs. Robinson posted something about the order of operations, but here it is again.
ReplyDelete"Ok. This will not work for EVERY problem you encounter but it will help I think.
1. Product/Quotient Rule (if it is not inside parenthesis)
2. Exponent Rule
3. Trig Rules/log rules, trig inverse rules, e rules
You work from the outside in. So if the quotient is inside a log you would skip to three because it would be inside parenthesis. Or if a fraction is raised to an exponent then you would default to step 2 because it is inside parenthesis. I hope this helps!"
So...I think the easiest way is to look at the left and right sides, compare the 2, see which rule you see first (the right side for exponents). Whichever rule you find first, write out EVERYTHING for that rule, then move on closer to the inside, and then right EVERYTHING out for that rule, and keep going until you're through. Then, simplify. I hope that wasn't too confusing! :)
When taking multiple derivitaves, you should always work from the outside in. When I do big ones, I make sure I have the derivitave of the first/most outer thing coppied down, then I cross it out so that I know I've already delt with that one. I then multiply that derivative by the next step I have to do, crossing it out in the problem, and so on until I am finished with the whole derivitave.
ReplyDeletewell, i started to make a list of what i have to do to the problem before i started working it. that helped me some. but yeah, like b-rob said,you work from the outside, then in. you should solve in this order, product/quotient rule, exponents, and then your trig/log/trig inverse/e rules.
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