Since a complex number in itself is a constant, its derivative is zero. They seem to get the point across very efficiently. You may want to review some of Sal's videos on derivatives - especially the ones where he graphs the derivatives intuitively. In sum, basically, the chain rule takes into consideration of how the functions within a function determine the function's slope at some input. That's the only time you will make sense of it all. Even when the slope of f(x) is 0 at x = -2, we see the graph of the derivative crosses the x-axis at x = -2.Ī lot of this has to do with looking at a graphs of a function and their derivatives on the same graphing sheet. we see that the x-value produces an incredibly negative y-value, which is the slope of the function f(x) at the x-value of interest (sometimes called a). and we know the derivative is decreasing. Towards the top of of the parabola on the left side, it almost looks like a straight line. then, if you graph 8x+4 on the same sheet of graphing paper. If you graph (2x+1)^2 you will see that it is a parabola. For free though I have to say nothing can beat Khanacademy.When you apply the chain rule, you're taking into account how the slope of the function is behaving by the influence of the internal variables. A tutor saved my butt for sure in my Algebra II class: we covered most of the curriculum for the whole semester in about two months. If you are willing to pay for it, you can probably find a good private math tutor in your area. If you're dedicated you can probably make it through the high school math curriculum in about 3-6 months, but it will require a lot of dedication on your part. I needed to know to succeed in Calculus in a very short amount of time. I wasn't really a "math person" until Calculus I in college when everything kind of clicked for me, and Khanacademy really helped me learn all of the algebra/geometry/trig/etc. I do have to give a HUGE shout out to Khanacademy. In my experience the SAT is designed, yes, to test your knowledge of these math courses, but also to challenge your critical thinking skills-problems will often be more abstract than those you find on Khanacademy or general math resources. I would also recommend getting a good SAT math prep book. However, I found that these classes were all actually quite slow in progress, and you could easily learn them all on Khanacademy within probably a few months to a year. We have Algebra I, Geometry, Algebra II, and then Precalculus (usually in that order), with one semester of class each. In the US-at least my state-it takes exactly 2 years for this. Update: I am thinking about getting the teaching textbook for algebra by Greg Sabouri and Shawn Sabouri, has anyone tried these books, how was your experience? Is it even possible to learn all of this math in this time span? I appreciate any helpful responses :) Does anyone know any good programs to learn from? (preferably something similar to kumon, but anything can help even if it requires self teaching like khan academy). I'm really behind my grade level and desperately need to catch up in order to be ready for the sats on time. Someone suggested going to kumon, does anyone know if this is a good program for this? Kumon seems to be for younger kids who are already going to school full time. I'm not going to self teach so I assume that would speed up the process, plus the added pressure of having to learn a certain thing by a certain date will help a bit. Now seeing how much I have to do has really gotten me out of my too relaxed state and I just want to learn. I haven't done math in two years not due to laziness, but due to the fact that my online school offers such basic math. Without all the pressure of due dates and now going at my own pace I've become too relaxed. That was two years ago, being homeschooled (starting freshman year) changed my work ethic to an extent. I've always been pretty good and hardworking in math and have never received less than an a in any of my classes. To give an insight about my work ethic/dedication I used to be in advanced math classes all the way until seventh grade (I went to private school which didn't offer advanced classes). Due to my homeschooling I have a lot of time to learn. I'm currently homeschooled and I would like to go to college in two years. I've previously learned algebra (wasn't the best, wasn't the worst) and have since forgotten most (basically all) of it.
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