Differentiation

/Tag: Differentiation
30 07, 2018

Differentiation

By |2018-07-30T10:00:07+10:00July 30th, 2018|Tags: , |Comments Off on Differentiation

Financial Maths Go to the Financial Maths Forum to see more questions or ask your own Topics Covered in Financial Maths Continuous Probability Distributions Normal Distribution Standard Normal Distribution Formulas used in Financial Maths  $$y=mx+b$$ $$m=\frac{rise}{run}$$ b = y-intercept [...]

13 07, 2016

Differential Equations

By |2016-11-01T13:44:29+10:00July 13th, 2016|Tags: , , , |0 Comments

Differential Equations worked examples `= lim_{hto 0},frac{(x+h)^2-1-(x^2-1)}h` `= lim_{hto 0},frac{x^2+2xh+h^2-1-x^2+1}h` `= lim_{hto 0},frac{2xh+h^2}h` `= lim_{hto 0}, 2x+h` = 2x + 0 = 2x `f'(x)= lim_{hto 0}frac{f(x+h)-f(x)}h` `= lim_{hto 0}frac{2(x+h)^3+1-(2x^3+1)}h` `= lim_{hto 0}frac{2x^3+6x^2h+6xh^2+2h^3-2x^3-1}h` `=lim_{hto 0}frac{6x^2h+6xh^2+2h^3}h` `=lim_{hto 0} 6x^2+6xh+2h^2` = 6x2 + 6x(0) + 2(0)2 [...]

14 08, 2015

First Principles

By |2017-09-09T09:17:39+10:00August 14th, 2015|Tags: , , , |0 Comments

First Principles $$f'(x)= \lim\limits_{h\to 0}\frac{f(x+h)-f(x)}h$$   worked examples Differentiate from First Principles x² + 2x. f(x) =  x² + 2x f(x + h) = (x + h)2 + 2(x + h) = x² + 2xh + h2 + 2x + 2h use the formula $$f'(x)= \lim\limits_{h\to 0}\frac{f(x+h)-f(x)}h$$ find  f(x + [...]

14 08, 2015

Surds & Fractions

By |2017-06-29T15:33:55+10:00August 14th, 2015|Tags: , , , |0 Comments

Surds & Fractions $$\frac{1}{x} = x^{-1}$$      $$\sqrt{x}=x^{\frac12}$$ worked examples Find the derivative of √(1 + 5t).  $$y = (1+5t)^{\frac12}$$ rewrite the square root as  indices $$y' = \frac12(1+5t)^{-\frac12}\,\times\,5$$ differentiate by bringing the half down, subtracting 1 and multiplying by the derivative of the inside bracket $$y' = [...]

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