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Mathematics

Mathematics. Session. Differentiation - 2. Session Objectives. Fundamental Rules, Product Rule and Quotient Rule Differentiation of Function of a Function Differentiation by Trigonometric Substitutions Differentiation of Implicit Functions Class Exercise. Fundamental Rules.

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Mathematics

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  1. Mathematics

  2. Session Differentiation - 2

  3. Session Objectives • Fundamental Rules, Product Rule and Quotient Rule • Differentiation of Function of a Function • Differentiation by Trigonometric Substitutions • Differentiation of Implicit Functions • Class Exercise

  4. Fundamental Rules

  5. Differentiate the following: Example-1

  6. Solution Differentiating y with respect to x, we get

  7. are differentiable functions, then If and Product Rule

  8. Differentiate: w.r.t. x. Example-2 Solution Let y =x2sinxlogx Differentiating w.r.t. x, we get

  9. , then are differentiable functions and If and Quotient Rule

  10. Differentiate: w.r.t. x. Example-3 Solution: Differentiating w.r.t. x, we get

  11. , then and Note: If Differentiation of Function of a Function If ƒ(x) and g(x) are differentiable functions, then ƒog is also differentiable (Chain Rule)

  12. Differentiate w. r. t. x. Example-4 Solution: Differentiating y w.r.t. x, we get

  13. Example-5

  14. Continued

  15. Trigonometric Substitutions

  16. Example-6 Solution: Putting x2 = cos2q

  17. Continued Differentiating y w.r.t. x, we get

  18. Example-7

  19. Continued

  20. Differentiation of Implicit Functions y is not expressible directly in terms of x

  21. Example-8 Solution: We have xy3 – yx3 = x

  22. Solution Cont.

  23. Thank you

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