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Mathematics with calculus mac301

Mathematics with calculus mac301. Course information Intro to Differentiation Review of year 12 skills Assignment 1. . Differentiation by Sight. Differentation. Derivative/ derived function/ gradient function f ’(x)=nax n-1 dy/dx=nax n-1. Function f(x)=ax n y= ax n.

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Mathematics with calculus mac301

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  1. Mathematics with calculus mac301 Course information Intro to Differentiation Review of year 12 skills Assignment 1.

  2. Differentiation by Sight Differentation • Derivative/ derived function/ gradient function • f ’(x)=naxn-1 • dy/dx=naxn-1 • Function • f(x)=axn • y= axn • To differentiate is to find the equation of the gradient function of any curve. • Gradients describe the instantaneous rate of change • The process of finding the derivative is called differentiation. • Functions that can be differentiated are said to be differentiable.

  3. Differentiation Review • Powers of x y = x3 y = x • Coefficients y = 4πx3 • Constant terms y=5 • Multiple terms y = x10-7x+5 • Products y=x2(2x7-6) • Quotients • Negative indices y = 3/x 7 • Surds/ fractional indices NB: The convention is to give answers in the same form as the question.

  4. Exercise 3.1C A1 (page 15) Differentiate the following functions: 1 2 3 4

  5. 5 6 7 8 9 10

  6. 1 Differentiate 11 11 11 ─ 1 = 10 x

  7. 2 Differentiate 3 2 3 ─ 1 = 3 x ─ 9

  8. 3 Differentiate 2 1 2  + 1 x + x + 1

  9. 4 Differentiate

  10. 5 Differentiate

  11. 6 Differentiate Write in index form:

  12. 7 Differentiate Expand Simplify

  13. 8 Differentiate Expand Simplify

  14. 9 Differentiate Divide through by (Multiply each term in the numerator by )

  15. 10 Differentiate Divide through by (Same as multiplying by )

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