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Differentiate the following

Differentiate the following. Chain Rule. How would you differentiate y = (x 3 +3) 2. Chain rule. If you have a function within a function then we need to use the chain rule If y = [f(x)] n then let u = f(x) and y = u n then, . Differentiate. y = (4x 3 – 7x) 6. Differentiate.

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Differentiate the following

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  1. Differentiate the following

  2. Chain Rule

  3. How would you differentiate y = (x3+3)2

  4. Chain rule • If you have a function within a function then we need to use the chain rule If y = [f(x)]n then let u = f(x) and y = un then,

  5. Differentiate • y = (4x3 – 7x)6

  6. Differentiate

  7. Find the equation of the tangent of y = (4x + 2)4 at the point (2, 1000)

  8. Easier way?

  9. Do we have to use the chain rule? • There is a quicker way to differentiate functions of functions than using the chain rule • What is it?

  10. y = (x+2)2 differentiates to 2(x+2) • y = (x2 +1)2 differentiates to 4x(x2+1) • y = (x2 + 2x)3 differentiates to 3(2x+2)(x2+2x)2 • Can you see the rule?

  11. Rule • If y = [f(x)]n then

  12. Differentiate y = (3x4 + 5)5

  13. Differentiate

  14. Find the value of dy/dx at (2, 1/3) if

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