Shreyas Mohan
2/18/2016 03:58:33 pm
The formal definition of a derivative:
Paige Eber
2/25/2016 04:09:36 pm
Heres an example problem;
Paige Eber
2/25/2016 04:10:21 pm
Heres an example problem;
Brandon C
2/18/2016 04:06:06 pm
The notation for taking a derivative of a function can be written in different ways:
Michelle H
2/18/2016 05:13:03 pm
The function for the derivative at a point x=a is...
Tanmayi K
2/18/2016 05:46:53 pm
Don't forget these derivatives of trig functions!
Paige Eber
2/23/2016 06:17:21 pm
An example problem of these is chapter 3.5 #2:
Taylor Garcia
2/18/2016 05:53:35 pm
There can not be a derivative at a point that is not continuous or differentiable. This includes graphs that have a corner (f(x)=x), a cusp (f(x)=x^(2/3)), vertical tangent(f(x)=x^(1/3)), or a discontinuity in the graph.
Rumi Venkatesh
2/18/2016 09:44:11 pm
The Derivatives of Exponential and Logarithmic Functions
Michelle H
2/25/2016 07:08:28 pm
Some examples of these situations: 2/18/2016 09:55:09 pm
A different way of looking at integrating e^x 2/18/2016 09:55:55 pm
sorry I meant taking the derivative of e^x, but integrating works with this joke too
Shreyas Mohan
2/18/2016 10:25:10 pm
Let's not forget the good old power rule!
Ananth Putcha
2/19/2016 08:50:06 pm
Some examples of these are...
Shreyas Mohan
2/18/2016 10:28:45 pm
Product Rule:
Paige Eber
2/22/2016 04:55:36 pm
An example of this is 3.3 #11
Shreyas Mohan
2/18/2016 10:31:45 pm
Quotient Rule:
Rachel Willy
2/22/2016 04:23:02 pm
We may have all memorized the trig function derivatives, but here is a way to prove the derivative of tan(x) = sec^2(x) using the quotient rule!
Christopher Glenn
2/18/2016 10:49:33 pm
I just thought I'd remind everyone of those inverse trig derivatives that I definitely memorized.
Shreyas Mohan
2/19/2016 07:08:12 pm
Here are some places where the derivative of a function may not exist:
Rachel Willy
2/19/2016 08:02:20 pm
When looking at a particle moving along a line or curve, don't forget these graphs and their derivative graphs!
Brandon C
2/19/2016 08:17:34 pm
Chain Rule 3.6 #7
Tanmayi K
2/19/2016 09:18:54 pm
Sometimes when finding derivatives, we must watch out for the domains. For example, if f(x) = ln (x4), the domain of f'x) is x>4 or (4,infinity) and f'(x) will = 1 / (x4). If x were less than 4, the derivative would be undefined.
Tanmayi K
2/19/2016 09:22:09 pm
Sometimes, life sucks and we have to differentiate implicitly.
Paige Eber
2/26/2016 06:19:41 pm
Heres an example of implicit differentiation;
Paige Eber
3/15/2016 07:11:01 pm
Another way to think about implicit differentiation is to consider the derivative of x to be dx and the derivative of y to be dy. Then, for example, the derivative of the function y^2 = x is 2ydy = dx and you divide by 2ydx to get dy/dx = 1/2y.
Christopher Glenn
2/19/2016 09:26:18 pm
Here's #9 from the chapter 3 review that blew my mind when I found out how to do it.
Rumi Venkatesh
2/19/2016 09:46:49 pm
Sum/Difference Rules
Tanmayi K
2/19/2016 10:17:35 pm
Don't forget about the constant multiple rule:
Juan Guevara
2/19/2016 10:23:16 pm
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Tanmayi K
2/19/2016 10:25:09 pm
3.3 #13
Shreyas Mohan
2/22/2016 05:08:24 pm
Implicit Differentiation:
Tanmayi K
2/22/2016 05:27:12 pm
On the ap test, we may be asked to match the graphs of functions with the graph of the functions derivative. For this, it is helpful to remember the derivative graph will have one less power. For example the derivative graph of a cubic function will be a parabola and the derivative graph of a parabola will be linear. It can also be helpful to locate where the graph equals zero on the derivative graph to be able to match it to a maximum or minimum on the graph of the function.
Michelle H
2/22/2016 05:31:42 pm
Differentiability implies continuity BUT continuity does not imply differentiability
Christopher Glenn
2/22/2016 06:57:10 pm
Here's a question from our 3.5  3.6 quiz.
Rumi Venkatesh
2/22/2016 07:17:14 pm
Find dy/dx of y=xsin(x)
Allison Y
2/22/2016 09:07:29 pm
3.3 #17
Shreyas Mohan
2/22/2016 09:08:07 pm
Chain Rule:
Taylor Garcia
2/22/2016 09:53:09 pm
3.3 #16
Juan Guevara
2/22/2016 11:39:10 pm
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Juan Guevara
2/22/2016 11:48:12 pm
p. 120 not 113
Rumi Venkatesh
2/23/2016 02:49:03 pm
3.5 #23
Michelle H
2/23/2016 06:06:08 pm
Ch. 3.5 #11
Brandon C
2/23/2016 07:37:34 pm
3.6 #12
Rachel Willy
2/23/2016 08:38:05 pm
3.6 #20
Taylor Garcia
2/23/2016 09:05:43 pm
3.8 #12
Allison Y
2/23/2016 10:07:56 pm
3.6 #8
Juan Guevara
2/23/2016 10:55:17 pm
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Juan Guevara
2/23/2016 10:58:27 pm
This is #19 not 18.
Juan Guevara
2/24/2016 01:09:54 pm
______________________________________________________
Rumi Venkatesh
2/24/2016 03:30:18 pm
Find dy/dx for the function y=(4x5)/3x^2
Paige Eber
2/24/2016 04:24:51 pm
3.6 #17
Taylor Garcia
2/24/2016 08:56:41 pm
3.6 #25
Allison Y
2/24/2016 09:08:23 pm
3.5 #7
Elise T
2/25/2016 02:23:27 pm
Intermediate Value Theorem for Derivatives:
Nathan Rao
2/25/2016 05:44:39 pm
Taking the derivative of a function with a constant to the power of a variable:
Allison Y
2/25/2016 06:21:07 pm
3.6 #11
Taylor Garcia
2/25/2016 07:50:16 pm
3.9 #31
Taylor Garcia
2/25/2016 09:07:22 pm
3.9 #17
Rumi Venkatesh
2/25/2016 10:03:21 pm
Find d^2y/dx^2 of y=(x^3+4x)^2
Brandon C
2/25/2016 10:41:51 pm
Connecting to Chapter 5, when you take the integral of a function, you are taking the antiderivative. This means that after you take the antiderivative, the derivative of the antiderivative should give you the function in the integral. This is an easy way to quickly check if the antiderivative you got is correct.
Juan Guevara
2/25/2016 11:30:59 pm
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Kavya Anjur
2/26/2016 10:22:09 pm
This is 3.1 #11, you start by using the formal definition of derivative by taking the limit as x approaches 0 of f(x+h)f(x)/h. You then plug in the corresponding numbers and variables based on the function. F(x+h) is equal to 2(x+h)^2  13(x+h) +5, and f(x) is 2x^2 13x +5. When you plug these into the derivative definition , you get the limit as h approaches 0 of (4xh + 2h^2 13h)/h, which simplifies to the minute as h approaches 0 of 4x +2h 13. When you substitute 0 for h based on the limit, you get 4x  13, so at x=3, the derivative is 4(3)  13, which is 1. The tangent line also passes through (3, 16), so it's equation is y = x  13.
Rumi Venkatesh
2/26/2016 10:33:34 pm
Find dy/dx for y=(4x^3)(2x^4)
Juan Guevara
2/26/2016 10:56:46 pm
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Juan Guevara
2/26/2016 10:58:31 pm
Wrong Chapter.
Rumi Venkatesh
3/1/2016 11:40:57 pm
Find dy^3/d^3x of y=3x^2
Shawn Park
3/2/2016 05:57:57 pm
3.6 HW #24
Michelle H
3/2/2016 07:46:06 pm
Don't forget that the derivative of e^x is e^x
Paige Eber
3/7/2016 06:34:25 pm
Chapter 3 Review Exercises #4
Brandon C
3/8/2016 10:58:27 pm
3.9 #40
Shawn Park
3/8/2016 11:17:08 pm
Semester 1 Calculus Review #4 3/9/2016 09:15:56 pm
Intuition for the formal definition of a derivative:
Shawn Park
3/10/2016 11:59:37 pm
3.6 #3
Herven
3/11/2016 11:19:27 pm
Chapter 3 Review Problem #36
Brandon C
3/14/2016 11:43:52 pm
Chapter 3 #4
Brandon C
3/14/2016 11:44:40 pm
3.5
Rachel Willy
3/15/2016 07:30:58 pm
3.7 #15
Rumi Venkatesh
3/15/2016 10:41:30 pm
3.6 #1
Rumi Venkatesh
3/18/2016 11:13:44 pm
Find dy/dx if y=e^cos(x)
Brandon C
3/22/2016 11:07:13 pm
3.6 #23
Brandon C
3/27/2016 09:20:46 pm
What is the derivative of ln(cosx)? Comments are closed.

AuthorMrs. Johnson's 20152016 BC Calculus Center for Review. By participating in this blog, you are indicating that the work that you submit is your own. If found to be otherwise true, you will not receive credit. Happy blogging!
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