# If k(x) =f (g(x)), then k’(x) = f ’ ( g(x) ) g’(x) k(x) = sin( x 2 ) k’(x) = cos ( x 2 ) 2x

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### Text of If k(x) =f (g(x)), then k’(x) = f ’ ( g(x) ) g’(x) k(x) = sin( x 2 ) k’(x) = cos ( x 2 ) 2x

• Slide 1
• If k(x) =f (g(x)), then k(x) = f ( g(x) ) g(x) k(x) = sin( x 2 ) k(x) = cos ( x 2 ) 2x
• Slide 2
• If y = sec(3 t), find y A. 3 sec(3 t) tan(3 t) B. 3 sec tan (3 t) C. sec(3 t) tan(3 t)
• Slide 3
• If y = sec(3 t), find y A. 3 sec(3 t) tan(3 t) B. 3 sec tan (3 t) C. sec(3 t) tan(3 t)
• Slide 4
• If y=tan(sin(x)), find y A. -sec 2 [sin(x)]cos(x) B. sec 2 [sin(x)]cos(x) C. sec 2 [cos(x)] D. -csc 2 [sin(x)]cos(x)
• Slide 5
• If y=tan(sin(x)), find y A. -sec 2 [sin(x)]cos(x) B. sec 2 [sin(x)]cos(x) C. sec 2 [cos(x)] D. -csc 2 [sin(x)]cos(x)
• Slide 6
• Corallary k(x) = g n (x) = [g(x)] n k(x) = n [g (x)] n-1 g(x)
• Slide 7
• If y=(2x+1) 4, find y A. 4(2) 3 B. 4(2x+1) 3 C. 8(2x+1) D. 8(2x+1) 3
• Slide 8
• If y=(2x+1) 4, find y A. 4(2) 3 B. 4(2x+1) 3 C. 8(2x+1) D. 8(2x+1) 3
• Slide 9
• If y=x cos(x 2 ), find dy/dx A. -x sin(x 2 ) + cos(x 2 ) B. -2x sin(x 2 ) + cos(x 2 ) C. -2x 2 sin(x 2 ) + cos(x 2 ) D. 2x 2 sin(x 2 ) + cos(x 2 )
• Slide 10
• If y=x cos(x 2 ), find dy/dx A. -x sin(x 2 ) + cos(x 2 ) B. -2x sin(x 2 ) + cos(x 2 ) C. -2x 2 sin(x 2 ) + cos(x 2 ) D. 2x 2 sin(x 2 ) + cos(x 2 )
• Slide 11
• The chain rule If y = sin(u) and u(x) = x 2 then dy/dx = dy/du du/dx dy/du = cos(u) du/dx = 2x dy/dx = cos(u) 2x = cos(x 2 ) 2x
• Slide 12
• The chain rule If y = cos(u) and u(x) = x 2 + 3x then dy/dx = dy/du du/dx dy/du = -sin(u) du/dx = 2x + 3 dy/dx = -sin(u) (2x+3) = -sin(x 2 +2x) (2x+3)
• Slide 13
• y=tan(u) u = 10x 5 find dy/dx A. -10 csc 2 (10x-5) B. sec 2 (10) C. -csc 2 (10x-5) D. 10 sec 2 (10x-5)
• Slide 14
• y=tan(u) u = 10x 5 find dy/dx A. -10 csc 2 (10x-5) B. sec 2 (10) C. -csc 2 (10x-5) D. 10 sec 2 (10x-5)
• Slide 15
• y= u 2 +u u = 10x 2 x find dy/dx A. (20 x 2 2x)(20x-1) B. (20 x 2 2x +1)20x C. (20 x 2 - 1)(20x-1) D. (20 x 2 2x +1)(20x-1)
• Slide 16
• y= u 2 +u u = 10x 2 x find dy/dx A. (20 x 2 2x)(20x-1) B. (20 x 2 2x +1)20x C. (20 x 2 - 1)(20x-1) D. (20 x 2 2x +1)(20x-1)
• Slide 17
• Corallary k(x) = [3x 3 - x -2 ] 20 k(x) = 20 [3x 3 - x -2 ] 19 (9x 2 +2x -3 )
• Slide 18
• Corallary y = [3x 3 - x -2 ] 20 let u = [3x 3 - x -2 ] let u = [3x 3 - x -2 ] du/dx = (9x 2 +2x -3 ) y=u 20 dy/dx=dy/du du/dx = 20u 19 du/dx du/dx = (9x 2 +2x -3 ) y=u 20 dy/dx=dy/du du/dx = 20u 19 du/dx = 20 [3x 3 - x -2 ] 19 (9x 2 +2x -3 ) = 20 [3x 3 - x -2 ] 19 (9x 2 +2x -3 )
• Slide 19
• If y = (sec(x)) 2 =sec 2 (x) find dy/dx A. 2 sec(x) tan(x) B. 2 sec 2 (x) tan(x) C. 2 sec(x) tan 2 (x) D. sec 2 (x) tan (x)
• Slide 20
• If y = (sec(x)) 2 =sec 2 (x) find dy/dx A. 2 sec(x) tan(x) B. 2 sec 2 (x) tan(x) C. 2 sec(x) tan 2 (x) D. sec 2 (x) tan (x)
• Slide 21
• Corallary =[3x 3 - x 2 ] 1/2 =[3x 3 - x 2 ] 1/2 k(x) = [3x 3 - x 2 ] -1/2 (9x 2 -2x)
• Slide 22
• Corallary k(x) =
• Slide 23
• Corallary
• Slide 24
• If y = find dy/dx A. csc 3/2 (x) B.. C.. D..
• Slide 25
• If y = find dy/dx A. csc 3/2 (x) B.. C.. D..
• Slide 26
• Corallary = [sin(2x) ] 1/2 = [sin(2x) ] 1/2 k(x) = [sin(2x)] -1/2 (cos(2x) 2)
• Slide 27
• k(x) = sec(sin(2x)) k(x) = sec(sin(2x))tan(sin(2x))(cos(2x) 2)
• Slide 28
• y = sec(sin(2x)) let u = sin(2x) dy/dx = dy/du du/dx y = sec u
• Slide 29
• y = sec(u) where u = sin(2x) dy/dx = dy/du du/dx = sec u tan u cos(2x) 2
• Slide 30
• y = sec(u) where u = sin(2x) dy/dx = dy/du du/dx = sec u tan u cos(2x) 2 sec(sin(2x))tan(sin(2x))(cos(2x) 2)
• Slide 31
• Number of heart beats per minute, t seconds after the beginning of a race is given by a) Find and explain. b) Find R(t). c) Find R(10) and explain. d) Find R(10) and explain.
• Slide 32
• Number of heart beats per minute, t seconds a) Find and explain.
• Slide 33
• Number of heart beats per minute, t seconds a) Find and explain.
• Slide 34
• Number of heart beats per minute, t seconds a) Find and explain.
• Slide 35
• Number of heart beats per minute, t seconds a) Find and explain. Marys maximum heart rate is 200 bpm = 220 age making her age close to 20.
• Slide 36
• Number of heart beats per minute, t seconds after the beginning of a race is given by a). b) Find R(t) c) Find R(10) = 115.47 bpm d) Find R(10) and explain.
• Slide 37
• Number of heart beats per minute, t seconds Find R(t)
• Slide 38
• Number of heart beats per minute, t seconds Find R(t) R(10) = 2.3094 bpm/min
• Slide 39
• quizz 1.Write the equation of the line tangent to the graph of y = x cos(x) when x=0. 2. Diff. g(x)=cot x [sin x cos x]. 3. Find the xs where the lines tangent to y= are horizontal.

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