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Chain Rule

Chain Rule. and Trig. What is to be learned?. How to apply the chain rule to trig functions. Type 1. y = sin(3x + 10). , where U = 3x + 10. let y = sin U. dy / du. du / dx. = 3. = cos U. = Cos U. dy / dx. 3. = 3Cos U. = 3Cos(3x + 10). The Chain Rule. Type sin (ax + b).

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Chain Rule

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  1. Chain Rule and Trig

  2. What is to be learned? • How to apply the chain rule to trig functions.

  3. Type 1 y = sin(3x + 10) , where U = 3x + 10 let y = sin U dy/du du/dx = 3 = cos U = Cos U dy/dx 3 = 3Cos U = 3Cos(3x + 10)

  4. The Chain Rule Type sin (ax + b) y = cos(2x – 12) , where U = 2x – 12 let y = cos U dy/du du/dx = 2 = -sin U = -Sin U 2 dy/dx = -2Sin U = -2Sin(2x – 12)

  5. And Finally same as (cosx)3 y = cos3x let y = u3 , where U = cosx dy/du = 3u2 du/dx = -sinx - sinx dy/dx = 3u2 = -3u2 sinx = -3cos2x sinx

  6. The Chain Rule i.e sin/cos with a power! Type (sinx)n y = sin4x same as (sinx)4 let y = u4 ,where u = sinx dy/du du/dx = 4u3 = cosx dy/dx = 4u3 cosx = 4u3 cosx = 4sin3x cosx

  7. These can be hard to spot Others examples y = √(10 + 4cosx) let y = U where U = 10 + 4cos x y = 5 ½ = (10 + 4cosx) ½ = 5(sinx)-1 ( )1 sinx let y = 5U-1 where U = sinx

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