10th post

This week in calculus was not to bad. In the beginning of the week we learned how to do implicit derivatives.
Steps:
1. Take the derivative
2. When you take the derivative of y, you put dy/dx behind it
3. Solve for dy/dx

An example of this would be:
6x^2+7y=9
(first take the derivative and put dy/dx behind the y derivative)

12x + 7 dy/dx=0
(now solve for dy/dx)

dy/dx= 12x/7

Another thing we learned this week is second implicit derivatives:
the steps are the same except after you solve for dy/dx, you are going to take the derivative of the function again and simplify it.

One thing i understood this week was related rates, its kind of like optimization but not as difficult lol. One way to simplify matters is to always write your given, then figure out what you are looking for. They may give you an equation and sometimes you may have to figure out one on your own. Once you have your equation, take the derivative in respect to time.

lets look at an example:

lets say they give you the radius r=6 and tell you r is increasing at a rate of 3 cm/sec.
You have to know the formula for area of a circle is A=(pie)r^2. Then they ask to find the rate of change of the area given these conditions.

First, take the derivative of the area formula

dA/dt= 2(pie)(6)(3)
dA/dt= 36(pie)
So your rate of change of area would be 36(pie), in related rates u basically plug into the formula, then take the derivative and solve for what they ask, in optimization your plugging into like 2 different things whereas related rates is mostly one formula and u look for one thing most of the time.

One thing i do not understand is angle elevation, i understand that it has the same concept as related rates considering the setup and the steps, i just do not understand how to find the information from looking at the triangle or solving the triangle. If someone can help me understand this it would help a lot. Thanks :)