Flashcards in Chapter 3 Deck (43)

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1

## What is the constant rule? (DxC=?)

### The derivative of a constant is always 0. (DxC=0)

2

## What is the derivative of x? (DxX=?)

### The derivative of x is 1. (DxX=1) (y=x)

3

## What is the power rule for derivatives? (DxX^n=?)

### The derivative of x^n is nx^(n-1). (DxX^n=nX^(n-1))

4

## What is the sum/difference rule? ((f+g)prime=?)

### The sum/difference of (f +/- g)prime is fprime +/-g prime.

5

## What is the derivative of a constant times a function of x? (DxCf(x)=?)

### The constant times the derivative of the function of x. (DxCf(x)=C*fprime(x))

6

## What is the definition of the number e?

### The number e is such that the lim h->0 (e^h-1)/h=1. (That the tangent slope of e^x at x=0 is 1)

7

## What is the product rule? ((f*g*l*m)prime)=?

### ((f*g*l*m)prime= fprime*g*l*m+f*gprime*l*m+f*g*lprime*m+f*g*l*mprime

8

## What is the quotient rule? (f/g)prime=?

### (f/g)prime=(fprime*g-f*gprime)/g^2

9

## DxSinx=?

### Cosx

10

## DxCosx=?

### -Sinx

11

## DxTanx=?

### Sec^2x

12

## DxCscx=?

### -CscxCotx

13

## DxSecx=?

### SecxTanx

14

## DxCotx=?

### -Csc^2x

15

## What is lim (theta)->0 Sin(theta)/(theta)?

### lim (theta)->0 Sin(theta)/(theta)=1

16

## What is lim (theta)->0 (Cos(theta)-1)/(theta)?

### lim (theta)->0 (Cos(theta)-1)/(theta)=0

17

## What is the Chain Rule? Dx(f o g)(x)=?

### The Chain Rule states that the derivative of (f o g)(x) is f(prime)(g(x))(gprime(x) (the derivative of the outside function with the inside function intact and still inside it multiplied by the derivative of the inside)

18

## What is the derivative of e^x?

### Dx e^x=e^x

19

## What is the derivative of e^f(x)?

### Dx e^f(x)=e^f(x)*fprime(x) (The derivative of e to the function f(x) is e to the function f(x) multiplied by the derivative of the function f(x)) (This comes from the chain rule)

20

## What is the method for implicit differentiation? What do you use this for

### Given an equation, find the prime (thinking of y(dx/dy) as f(x))(use the chain rule for substituting), and then solve for dx/dy. With the found equation, you can find the slope of the tangent line at a given point by plugging in values of the given point.

21

## DxSin^-1(x)=?

### DxSin^-1(x)= 1/√(1-x^2)

22

## DxCos^-1(x)=?

### DxCos^-1(x)= -1/√(1-x^2)

23

## DxSec^-1(x)=?

### DxSec^-1(x)= 1/x√(x^2-1)

24

## DxCsc^-1(x)=?

### DxCsc^-1(x)= -1/x√(x^2-1)

25

## DxCot^-1(x)=?

### DxCot^-1(x)= -1/(x^2+1)

26

## DxTan^-1(x)=?

### DxTan^-1(x)=1/(x^2+1)

27

## What is the Derivation of Log sub a of x? DxLogaX=?

### The Derivation of the Log sub a of x is 1/xlna. DxLogaX= 1/((x)lna)

28

## What is the Derivation of the Natural log of x? DxLnx=?

### The Derivation of the Natural log of x is 1/x. Dxlnx=1/x

29

## What is the Derivation of Log sub a of f(x)? DxLogaF(x)=?

### The Derivation of Log sub a of f(x) is 1/(f(x) *lna)*fprime(x). DxlogaF(x)=1/(f(x)*lna)*fprime(x)

30

## What is the Derivation of the Natural log of f(x)? DxLnf(x)=?

### The Derivation of the Natural log of f(x) is 1/f(x) *fprime(x). DxLnf(x)=1/f(x) *fprime(x)

31

## What is Logarithmic Differentiation? How do you use it? When do you use it?

###
Logarithmic Differentiation is using the properties of logarithms and Implicit Differentiation to find dy/dx. 1st take the ln of both sides, then simplify the Right Hand Side, then use Implicit Differentiation. If y is on the RHS, substitute the given y for it.

You use it when there is a function x to the power of another function x.

32

## What is the equation for the area of the circle?

### A=pi(r)^2

33

## How do you evaluate a limit at infinity? (Chapter 2 Review)

### You multiply both the numerator and the denominator by 1/x^n if n is the highest power of x found in the denominator

34

## What is the equation for the volume of a sphere?

### V=4/3pi(r)^3

35

## How do you calculate Average Rate of Change? (Chapter 2 Review)

### Its just the slope formula ya dummy

36

## What is the equation for the surface area of a sphere?

### 4pi(r)^2

37

## What is the equation for the volume of a cone?

### (pi(r)^2)*(h/3)

38

## How do you find theta using trig?

### Soh-Cah-Toa, (if opposite side is 4 and adjacent side is 3, sin(theta)=4/3)

39

## What is the derivative of n^x?

### Dx n^x=N^x*lnx*fprime(x)

40

## What is the Law of Cosines? (For not a right triangle)

### c^2=a^2+b^2-2(a)(b)(CosC)

41

## What is the Law of Sines? (For not a right triangle)

### SinA/a=SinB/b=SinC/c

42

## What is the definition of the "Normal Line" in relation to the tangent line?

### The Normal Line is the line that is perpendicular to the tangent line at the point of tangency

43