CK-12-Calculus

2.3. Techniques of Differentiation http://www.ck12.org Example 8: Finddy/dxfor y=x (^2) − 5 x^3 + 2 Solution: dy dx= d dx [x (^2 ...

http://www.ck12.org Chapter 2. Derivatives The second derivative, f′′, can also be written asddx^2 y 2 , and f′′′can be written ...

2.3. Techniques of Differentiation http://www.ck12.org 6.y= (x^3 − 3 x^2 +x)( 2 x^3 + 7 x^4 ) 7.y= (^1 x+x^12 )( 3 x^4 − 7 ) 8.y ...

http://www.ck12.org Chapter 2. Derivatives 2.4 Derivatives of Trigonometric Functions Learning Objectives A student will be able ...

2.4. Derivatives of Trigonometric Functions http://www.ck12.org The derivatives of the remaining trigonometric functions are sho ...

http://www.ck12.org Chapter 2. Derivatives f′(x) =x^2 (−sinx)+ 2 xcosx+cosx =−x^2 sinx+ 2 xcosx+cosx. Example 3: Finddy/dxify= 1 ...

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 ...