So, i haven't been to school in a few days..so i'm going to explain a few throwback things that noone has talked about in a while.
Lets start with chain rule:
outside to inside is the major hint..
such as cos(2s)
first derivative of cosine, then the derivative of 2s, multiply them togeter..and presto.
Now, lets talk about product rule with chain rule:
Make sure if you have xcos2x, you use product rule. How do you know to use product rule? You are multiplying two terms with variables.
(derivative of first)(copy second) + (derivative of second)(copy first)
*when you take the derivative of cos2x, make sure to include the chain rule!
Things i always misunderstand
*tangent lines, i can't decide waht to do for these.
*related rates
*optimization..
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Tangent lines are simple.
ReplyDeleteAll you do is take the derivative of the function...plug in the x value of the point they gave you. This gives you the slope, m.
Now you plug into slope-point formula:
y-y1 = m(x-x1) where the point they gave you is (x1, y1).
For tangent line, you're really only taking a derivative. If the problem doesn't give you x and y, solve for x, then plug x back in to find y. Once you have your x and y you need to take the derivative of the function given. After that, you plug in x to find your slope. Once you have your slope, you have all you need to form your tangent line. All you have to do is plug into point slope form, and you're good to go.
ReplyDeleteheres the steps for tangent lines:
ReplyDeletetake the first der. plug in x and solve for it. you getslope and plug into point slope formula
If you need a y value, plug the x value into the original function and solve. To find the slope, take the derivative of the original function. Then plug in the x value and solve to find the slope. Then plug into point slope form y-y1=slope(x-x1). Hope this helps!
ReplyDeleteif i remember correctly, for optimization, the problem has two different equations, a primary and secondary equation, and you draw a picture and use those to solve the problem. lol
ReplyDeleteSteps for Related Rates:
ReplyDeleteMake a sketch of the problem
Identify constant and variable quantities
Establish relationship between quantities.
Differentiate w/ respect to time.
Finish solving.