Alright, so...this week was extremely tough. I think most people probably agree on that, haha. We learned about finding equations for a tangent line, normal line, the points where y has horizontal tangents, and we worked on arc trig derivative formulas. I'm having so much trouble with solving the problem after I get the derivative, and I don't know why.
At least I get one thing we learned. It was finding the equation of the tangent line.
For example: (x^3-3x-1)(x+2) and given the point (1,-3)
First you just follow the product rule for the derivative: (x^3-3x-1)(1)+(x+2)(3x^2-3)
= (x^3-3x-1)+(3x^4-3x+6x^2-6) = 3x^4+x^3+6x^2-6x-7
Next plug in your x, which is 1: 3(1)^4+(1)^3+6(1)^2-6(1)-7 = 3+6-6-7 = -4
Finally, plug in to the point slope form: y+3=-4(x-1)
Something I am confused on is the horizontal tangents.
For example: y=3x^3+4x^2+5 at (1,12) So I understand how to get 9x^2+8x=0
But then what's next? How do I get the points?
Also, can someone help me on how to solve: arcsin3x/x ?
That would be the quotient rule. In the second part of the formula I'm suppose to copy the top, but I'm not suppose to have trig in the problem. So, do I take the derivative of it anyway? Or is there something else I'm suppose to do?
Overall, my confusion is mainly on simplifying these arc trig formulas once I have the derivative. They just seem massive and complicated. And then I get aggravated with it and give up. Hopefully, I get it by the test ha.
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arcsin3x/x
ReplyDelete1/sqrt((1-3x/x)^2) i think you get that
then you multiply that by u'
u' simply equals the quotient rule of 3x/x = (x)(3) - (3x)(1) / x^2 = 3x - 3x / x^2 = 0 / x^2 = O
You should probably get me to explain it one more time...hahah.
ReplyDeleteAfter you plug it into your formula and have that nasty fraction times the derivative, you just have to see what you can combine. Try to see if anything would cancel..probably not, because we aren't that lucky; but still try. Then just think of ways to multiply them together..and if you think to yourself that you don't know how to multiply those things..that means you're done and stop stressing.. :)
you should plug in your derivative..you also need to make sure that theres nothing you can combine.then after that cancel whatever can be cancelled and try to put them together.and then whats left is your answer.
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