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Derivatives

Derivatives. Becoming an expert at derivatives in a few easy steps!. Gettin g Started (Click on a picture to get around). Definition. Examples. Understand the origin of Derivatives See the basic format for calculating the derivatives. Basic Trigonometric The natural log. Quiz.

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Derivatives

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  1. Derivatives Becoming an expert at derivatives in a few easy steps!

  2. GettingStarted(Click on a picture to get around) Definition Examples • Understand the origin of Derivatives • See the basic format for calculating the derivatives. • Basic • Trigonometric • The natural log Quiz

  3. Long Definition Dictionary Definition: Change of function:the limit approached in the ratio of a function and its variable, as the variable is changed ever more infinitesimally Mathematically: df/dx = f’(x)= y’ It’s all the same. Just a different way of writing it! (it looks complicated but don’t worry!)

  4. Basic Format y=f(x)=ax+b y’=f’(x)= a • Where ‘a’ is a constant and b is a different constant • If f(x) has only one value of x then then derivative is always the constant in front of x. F(x)= a F’(x)= 0 • If f(x) is a constant, the derivative is always 0.

  5. Basic Format Cont'd… F(x)= xa F’(x)= axa-1 The basic form of a derivative is given x raised to a power of ‘a’ (a constant), the derivative is ‘a’ times x to the power of (x-1).

  6. Simple Examples 1) y=2x 2) y=356 y’= 2 y’= 0 3) y= x3 4) y= 3x2 y’= 3x2 y’= 6x 1) You only have one x so the value is the constant 2) y=a constant so y’=0 automatically 3) You have to move 3 to the front of x and change to power of x to (3-1) 4) The only difference between ex 3 is that when you bring the 2 down, you need to multiply it by the 3 that is already there.

  7. Trig. Examples 1) y= sinx 2) y=cosx y’= cosx y’= -sinx 3) y= tanx 4) y= cotx y’= sec2x y’= -csc2x For all of these you just need to memorize the basic formulas shown to the right to be able to do more complicated problems.

  8. The Natural Log (ln) 1) y=ln(x) 2) y= ln(x2+2) y’= 1/x y’= 2x/(x2 +2) There is a trick to ln problems… Step 1: first take 1 divided by the value in parentheses Step 2: times step 1 by the derivative of everything in the parentheses (for ex.2 it would be the derivative of (x2+2) which equals 2x)

  9. Quiz Time!!!!!! Find the Derivative of y=2x + 4 A. 2x + 4 B. 2 +x C. 2 D. X + 4

  10. Nope but good guess. TRY AGAIN!!!

  11. Correct!!!!! You are amazing!

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