CK-12-Calculus

2.1. Tangent Lines and Rates of Change http://www.ck12.org a tree, it would not be his average speed that determines his surviva ...

http://www.ck12.org Chapter 2. Derivatives Figure 2 msec= f(t^1 t 1 )−−tf 0 (t^0 ) Instantaneous Rate of Change The instantaneou ...

2.1. Tangent Lines and Rates of Change http://www.ck12.org Example 4: Suppose thaty=x^2 − 3. Find the average rate of change of ...

http://www.ck12.org Chapter 2. Derivatives MEDIA Click image to the left for use the URL below. URL: http://www.ck12.org/flx/ren ...

2.2. The Derivative http://www.ck12.org 2.2 The Derivative Learning Objectives A student will be able to: Demonstrate an unders ...

http://www.ck12.org Chapter 2. Derivatives f′(x) =limh→ 01 h [ x+h x+h+ 1 − x x+ 1 ] =limh→ (^01) h [(x+h)(x+ 1 )−x(x+h+ 1 ) (x+ ...

2.2. The Derivative http://www.ck12.org y−y 0 =m(x−x 0 ) y− 1 =^12 (x− 1 ) y=^12 x+^12. Notation Calculus, just like all branche ...

http://www.ck12.org Chapter 2. Derivatives Figure 4 Figure 5 ...

2.2. The Derivative http://www.ck12.org Figure 6 Figure 7 Many functions in mathematics do not have corners, cusps, vertical tan ...

http://www.ck12.org Chapter 2. Derivatives Multimedia Links For an introduction to the derivative(4.0)(4.1), see Math Video Tuto ...

2.3. Techniques of Differentiation http://www.ck12.org 2.3 Techniques of Differentiation Learning Objectives A student will be a ...

http://www.ck12.org Chapter 2. Derivatives Note that this proof depends on using the binomial theorem from precalculus. Example ...

2.3. Techniques of Differentiation http://www.ck12.org and d dx[f(x)−g(x)] = d dx[f(x)]− d dx[g(x)]. In simpler notation, (f±g)′ ...

http://www.ck12.org Chapter 2. Derivatives Finddydxfory= ( 3 x^4 + 2 )( 7 x^3 − 1 ). Solution: There are two methods to solve th ...

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 ...