Warmup 11/12/15 Work on your personal Bible study. As you do so, keep an open mind for what lessons God may want you to learn today. To see how to take the derivative of a quotient pp 222: 2, 3, 4, 6, 9 Objective Tonight’s Homework

Homework Help Let’s spend the first 10 minutes of class going over any problems with which you need help.

Notes on Derivative of a Quotient We saw that the derivative of a product can be written as this: f’(uv) = udv + vdu Let’s find a similar rule for a quotient.

Notes on Derivative of a Quotient Example: Find the derivative of… x/y

Notes on Derivative of a Quotient Example: Find the derivative of… x/y This is the same thing as. x1/y OR xy -1

Notes on Derivative of a Quotient Example: Find the derivative of… x/y This is the same thing as. x1/y OR xy -1 Derivative of this is: x-1y -2 dy + y -1 1 dx

Notes on Derivative of a Quotient Example: Find the derivative of… x/y This is the same thing as. x1/y OR xy -1 Derivative of this is: x-1y -2 dy + y -1 1 dx Let’s clean this up a bit. -x dy dx -x dy y dx y dx – x dy y 2 y y 2 y 2 y 2 +

Notes on Derivative of a Quotient Now, this example worked for specific functions, but it turns out it works for generic functions as well! Derivative of a Quotient: Given 2 functions, u and v, the derivative is… d( ) = To remember, we say “low dee high minus high dee low, all over the square of what’s below” u v du – u dv v v 2

Notes on Derivative of a Quotient Example: Find the derivative of sin(x) / cos(x)

Notes on Derivative of a Quotient Example: Find the derivative of sin(x) / cos(x) cos(x)cos(x) – sin(x)(-sin(x)) cos 2 (x) cos 2 (x) + sin 2 (x) cos 2 (x) 1 / cos 2 (x) dy/dx tan(x) = sec 2 (x) This lines up with what is true!

Group Practice Look at the example problems on pages 220 and 221. Make sure the examples make sense. Work through them with a friend. Then look at the homework tonight and see if there are any problems you think will be hard. Now is the time to ask a friend or the teacher for help! pp 222: 2, 3, 4, 6, 9

Exit Question Derivative of x/y = ? a) (y dx – x dy) / y 2 b) (x dy – y dx) / y 2 c) (y dx – x dy) / x 2 d) (x dy – y dx) / x 2 e) None of the above