I started this week off really confused but by Friday I was only slightly confused. The thing I understand the most is quotient rule. The formula for quotient rule is vu^1-uv^1/v^2 or the derivative of the top times the bottom – the derivative of the bottom times the top over the bottom squared. An example is sin x / x-1. Take the derivative of the top which is (cos x) times the bottom (x-1) – the derivative of the bottom (1) times the top (sin x) over the bottom squared (x-1) ^2. From there, it is just simple algebra. The answer comes out to (cos x) (x-1)-sin x/(x-1) ^2. You do not use quotient rule when there is only an x on the bottom. You just bring the x to the top and make the exponent negative then use the formula U^n.
The thing I am most confused about is when to or when not to use the product rule. I understand you use it when you’re multiplying obviously, but do you only use it when you’re multiplying quadratics and trig functions? I know you don’t use it when you are multiplying 8 cos x so I’m thinking if there is a number in the problem you do not use product rule but does that apply to all problems? I also get confused when there is a problem such as x (quadratic). I don’t know if I have to distribute the x or use product rule and take the derivative of the x. I also struggled with problems like x^2 x^-5^3+1/2x^4pi^3 or number 45 on our first packet, whether I can simplify an answer or not, and the wording on some problems, but I think I will eventually catch on with more practice. All in all this week has been overwhelming but I’m looking forward to spending the year with everyone.
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ReplyDeletei'm pretty sure that the only way you can use product rule for trig functions is if you have something like x^2cos(x). In that case, you would consider x^2 your first term and cos(x) your second term
ReplyDeleteYou can also use it with sin(x)cos(x) any time you have two separate EQUATIONS being multiplied.
ReplyDeletei think you can use the product rule for only certain trig functions like x^2sin(x. therefore you use x^2 as the first term and sin(x) as your second.
ReplyDeleteyou use the product rule when you're multiplying two terms..like x(x+4) or (x^2 +4x+ 20)(x+3) or anything like that. To use the product rule you have to copy the first times derivative of the second plus copy the second times derivative of the first then you just use algebra to solve the rest of the way.
ReplyDeleteTo solve quadratics you just multiply the exponent times the coefficient of whatever term you are working on and then subtract one from the exponent.