First of all, Happy Halloween!
What a busy week in AP Calc, we continued on with practicing the chain rule and derivatives by learning Implicit Differentiation, derivatives of Inverse Trigonometric Functions, and derivatives of Exponential and Logarithmic Functions.
The process by which we find dy/dx is called implicit differentiation. You simplify both sides of the equation with respect to x, treating y as a differentiable function of x and apply the chain rule.
Implicit differentiation was quite confusing to understand at first but once you applied all the past knowledge and followed the steps of implicit differentiation, the answer came easily.
One thing that was interesting about implicit differentiation was being able to collect terms in order to simplify the dy/dx more. (Example below.)
Finding the derivatives of inverse trig functions... Oh boy.
This wasn't too bad, you just had to use the given equations (above) and insert the x in there. It just got a little messy when simplifying the equations; this is a little challenging for me because I'm not sure what we can and cannot do sometimes. I feel like my mind doesn't think out of the box when it comes to simplification, someone has to show me that we are allowed to move things around and then I will feel dumbfounded that I couldn't think of doing that before. Anyways, this section also included using implicit differentiation.
Finding the derivatives of exponential and logarithmic functions is quite simple, just a couple rules to remember!
It is that time again... To take the chapter test. We are now doing a review assignment and practicing things such as simply finding the derivative with addition. I felt very flustered because I don't feel ready at all for the test.. I always do masteries... But I was able to have some one on one tutoring with Miss Krauss and now I feel so much better; she walked through all the little steps with me, it is very important for me to know all the little steps that happened to find the answer or I will become confused. So it was cool to have her review with me, I feel a little better and will continue to practice and review until the chapter test! Sometimes I feel like I understand things very well, then I look at a new problem and it seems foreign. Anyways, a tip from Miss Krauss was to use different colored pens to stay organized; this was a great strategy in solving these problems!