By Niko Surace For kids in Calculus Subject: Mathematics Go to
index Lets Do Math
Slide 3
* What is a derivative What is a derivative * Why it is
Important Why it is Important * Notations of Derivatives Notations
of Derivatives * Differentiation (Difference Quotient)
Differentiation (Difference Quotient) * Constant and Power Rule
Constant and Power Rule * Sum/Difference Rule Sum/Difference Rule *
Product Rule Product Rule * Quotient Rule Quotient Rule * Chain
Rule Chain Rule * Trigonometric Functions Trigonometric Functions *
Quiz Your Self Quiz Your Self Click on a link to go to a page to
learn about derivatives and then take the quiz
Slide 4
* A derivative is in a branch of Mathematics called Calculus.
The derivative is the measure of how a function changes as its
input changes. It tells what the slope is at any point on a graph
as well. It is one of the two properties of single variable
calculus. * Back to Index Back to Index
Slide 5
* The importance of the derivatives is vital for the world
today. Derivatives can tell such things like how fast some one was
going, the acceleration they were experiencing, and where they were
with just one equation. It also gave us the a way to prove all of
the volume equations in the world. * Back to Index Back to
Index
Slide 6
* There many ways to see the same notation for derivatives.
Great mathematical minds used different ways to say the same thing.
In class we will use Leibniz notation. * This means that dy/dx is
the notation for a derivative * For multiple derviatives there is a
power to d so for example the second derivative would be written as
d 2 y/dx 2 * Back to Index Back to Index
Slide 7
* The difference quotient is what is formally used to find a
derivative. The difference quotient is a math equation that finds
the limit as x approaches a certain x value. The difference
quotient is shown below. * An example of difference quotient * Back
to Index Back to Index
Slide 8
* The constant rule is used as an informal way to find the
derivative. The constant rule says that any constant number when
taking the derivative of it equals 0 * For instance the derivative
of 5 = 0 * The power rule is a short cut to find derivatives quick
and easy. The rule states that you take the exponent of any number
and multiply it by the number and subtract one from the exponent
itself. * Some examples * Back to Index Back to Index
Slide 9
* The sum and difference rule are another informal way of
finding a derivative. The sum and difference rule states that you
can break up any equation by a plus or minus sign to find the
derivative. * For instance x 2 +5 could be broken up to be d/dx x 2
+ d/dx 5 * Back to Index Back to Index
Slide 10
* The Product Rule is another informal way to do derivatives.
The product rule as the name implies is used when taking the
derivative of two things that are being multiplied together * For
instance find the d/dx of xy * The product rule is f(x)g I (x) +
g(x)f I (x) * An Example * Back to Index Back to Index
Slide 11
* The quotient rule is also an informal way to find the
derivative. It is used when to functions are divided together * For
instance (x 2 + 5)/(x+4) is two functions that would be perfect for
the quotient rule * The quotient rule is (g(x)f I (x) f(x)g I (x))
/ (g(x)) 2 * Back to Index Back to Index
Slide 12
* The chain rule is the Golden Rule. It is the rule to rule all
rules. The chain rule states that for any function inside another
function you take the derivative of the inside function and
multiply it by the derivative of the outside function * For
instance find d/dx of (x 2 + 5x 2 ) 2 * The chain rule is * Back to
Index Back to Index
Slide 13
* You can take the derivative of trigonometric functions. They
are always continuous and follow a pattern. This the pattern that
you follow for trig functions * d/dx sin(x)= cos(x) * d/dx cos(x)=
-sin(x) * d/dx tan(x)= sec 2 (x) * d/dx csc(x)= -csc(x)cot(x) *
d/dx sec(x)= sec(x)tan(x) * d/dx cot(x)= -csc 2 (x) * Back to Index
Back to Index
Slide 14
* Click Click here to begin Quiz * Back Back to Index
Slide 15
* 1) Find d/dx of x 2 + 7 * A. d/dx = 2x +7 A. * B. d/dx = 2x
B. * C. d/dx = x 2 C. * D. d/dx = x 2 + 7 D. Back to begin
quiz
Slide 16
* is not the right answer * Remember to use your rules and
check you math and take your time * Back to Question Back to
Question
Slide 17
* is the correct answer * When you take the derivative of x 2
using your power rule you get 2x and since 7 is a constant its
derivative is 0 so your answer is 2x * Next Question Next
Question
Slide 18
* is not the right answer * Remember to use your rules and
check your math and take your time * Back to Question Back to
Question
Slide 19
* is not the right answer * Remember to use your rules and
check your math and take your time * Back to Question Back to
Question
Slide 20
* Find d/dx of (x 2 +5) 3 * A. d/dx = x 6 + 125 A. * B. d/dx =
6(x 2 + 5) 3 B. * C. d/dx = 6x(x 2 + 5) 2 C. * D. d/dx = 3(x 2 +5)
2 D.
Slide 21
* is not the right answer * Remember to use your rules and
check you math and take your time * Back to Question Back to
Question
Slide 22
* is not the right answer * Remember to use your rules and
check your math and take your time * Back to Question Back to
Question
Slide 23
* is the correct answer * When you take the derivative of (x 2
+5) 3 you have to use the chain rule and power rule functions. When
you take the derivative of the inside you get 2x. You have to
multiply it by the derivative of the outside function which is 3(x
2 +5) 2 which you should get with your power rule. This gives you
the answer of 6x(x 2 +5) 2 * Next Question Next Question
Slide 24
* is not the right answer * Remember to use your rules and
check your math and take your time * Back to Question Back to
Question
Slide 25
* Find d/dx of (x+5)(x+6) * A. x 2 + 11x +30 A. * B. 2x + 11 B.
* C. (x+5) (x+6) C. * D. 1 D.
Slide 26
* is not the right answer * Remember to use your rules and
check you math and take your time * Back to Question Back to
Question
Slide 27
* is the correct answer * When you take the derivative of (x
+5)(x+6) you have to use the product rule to figure it out. You
have to take the derivative of both functions multiply them by the
other function and then add them together. * 1(x+5) + 1(x+6) = 2x
+11 * Next Question Next Question
Slide 28
* is not the right answer * Remember to use your rules and
check your math and take your time * Back to Question Back to
Question
Slide 29
* is not the right answer * Remember to use your rules and
check your math and take your time * Back to Question Back to
Question
Slide 30
* Find d/dx of (x+7)/(x+3) * A. 2x+10 A. * B.
((x+7)(x+3))/(x-3) 2 B. * C. (x+3)/(x+7) C. * D. 4/(x+3) 2 D.
Slide 31
* is not the right answer * Remember to use your rules and
check you math and take your time * Back to Question Back to
Question
Slide 32
* is not the right answer * Remember to use your rules and
check your math and take your time * Back to Question Back to
Question
Slide 33
* is not the right answer * Remember to use your rules and
check your math and take your time * Back to Question Back to
Question
Slide 34
* is the correct answer * When you take the derivative of (x
+7)/(x+3) you have to use the quotient rule to figure it out. You
have to take the derivative of both functions multiply them by the
other function and then then subtract them by the rule and divide
the differnce by the bottom squared * (1(x+7) - 1(x+3))/ (x+3) 2 =
4/(x+3) 2 * Next Question Next Question
Slide 35
* Find d/dx of sin(6x) + 5 * A. 6cos(6x) A. * B. 6sin(6x) + 5
B. * C. 6cos(6x) + 5 C. * D. 6sin(6x) D.
Slide 36
* is the correct answer * When you take the derivative of a
trig function you have to use the chain rule and remember the
derivative for each * Sin(6x) = 6 * cos(6x) * End Quiz End
Quiz
Slide 37
* is not the right answer * Remember to use your rules and
check your math and take your time * Back to Question Back to
Question
Slide 38
* is not the right answer * Remember to use your rules and
check your math and take your time * Back to Question Back to
Question
Slide 39
* is not the right answer * Remember to use your rules and
check you math and take your time * Back to Question Back to
Question
Slide 40
* If you have any questions come and ask me. I will help you
with anything I can. If anything is unclear dont be afraid to ask
me and I will explain it better. * Click here when done Click here
when done