CK-12-Calculus

2.4. Derivatives of Trigonometric Functions http://www.ck12.org Multimedia Links For examples of finding the derivatives of trig ...

http://www.ck12.org Chapter 2. Derivatives 2.5 The Chain Rule Learning Objectives A student will be able to: Know the chain rul ...

2.5. The Chain Rule http://www.ck12.org y= [u(x)]n. The rule for differentiating such functions is called theGeneral Power Rule. ...

http://www.ck12.org Chapter 2. Derivatives Finddy/dxfory=sin^3 x. Solution: The function can be written asy= [sinx]^3 .Thus dy d ...

2.5. The Chain Rule http://www.ck12.org Multimedia Links For an introduction to the Chain Rule(5.0), see Khan Academy, Calculus: ...

http://www.ck12.org Chapter 2. Derivatives f(x) =( 2 xx−−^35 )^3 ...

2.6. Implicit Differentiation http://www.ck12.org 2.6 Implicit Differentiation Learning Objectives A student will be able to: F ...

http://www.ck12.org Chapter 2. Derivatives But sincey= 21 x, substitution gives dy dx= − 1 x( 2 x) = 2 −x^12. which agrees with ...

2.6. Implicit Differentiation http://www.ck12.org First we need to use implicit differentiation to finddy/dxand then substitute ...

http://www.ck12.org Chapter 2. Derivatives Use implicit differentiation to findd^2 y/dx^2 if 5x^2 − 4 y^2 = 9 .Also find ddx^2 y ...

2.6. Implicit Differentiation http://www.ck12.org Multimedia Links For more examples of implicit differentiation(6.0), see Math ...

http://www.ck12.org Chapter 2. Derivatives 7.x^2 y−y^2 x=0 at( 1 , 1 ) sin(xy) =yat(π 2 , 1 ) Findy′′by implicit differentiatio ...

2.7. Linearization and Newton’s Method http://www.ck12.org 2.7 Linearization and Newton’s Method Learning Objectives A student w ...

http://www.ck12.org Chapter 2. Derivatives Figure 8a Figure 8b So for values ofxclose tox 0 , the values ofyof this tangent line ...

2.7. Linearization and Newton’s Method http://www.ck12.org is a linearization offnearx 0. Example 1: Find the linearization off( ...

http://www.ck12.org Chapter 2. Derivatives f(x)≈ √ 3 2 + 1 2 ( x−π 3 ) ≈ √ 3 2 + x 2 − π 6 ≈x 2 + 0. 343. Figure 10 Newton’s Met ...

2.7. Linearization and Newton’s Method http://www.ck12.org f(x)≈f(x 0 )+f′(x 0 )(x−x 0 ) ≈− 1 +( 4 )(x− 2 ) ≈− 1 + 4 x− 8 ≈ 4 x− ...

http://www.ck12.org Chapter 2. Derivatives Guess the first approximation to a solution of the equationf(x) =0. A graph would be ...

2.7. Linearization and Newton’s Method http://www.ck12.org Figure 11 xn+ 1 =xn−x (^3) n+xn− 1 3 x^2 n+ 1 x 2 = 0. 6 −(^0.^6 ) (^ ...

http://www.ck12.org Chapter 2. Derivatives Review Questions Find the linearization of f(x) =x (^2) + 1 x ata=1. Find the line ...