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/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||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 [...]

20 06, 2016

## e Product Rule

By |2016-11-03T08:05:57+10:00June 20th, 2016||0 Comments

Differentiating Exponentials with Product Rule y = ex , y' = ex y = eax, y' = aeax $y'=vu'-uv'$ worked examples Differentiate with respect to x  $y=xe^x$. y'= ex . 1 + x . ex   Produtc Rule $y'=vu'-uv'$ where u = x    u ' = 1 v = ex  [...]

14 08, 2015

## Normals

By |2017-06-29T15:37:25+10:00August 14th, 2015||0 Comments

Normals worked examples Show that the equation of the normal to the curve y = x3 - 5x at the point (1, -4) is given by x - 2y - 9 = 0 y' = 3x2 - 5 find the first derivative so we can get the gradient [...]

14 08, 2015

## Tangents

By |2016-11-01T13:58:36+10:00August 14th, 2015||0 Comments

Tangents worked examples y = x³ - 3x² - 9x + 1,  find the equation of the inflexional tangent. y' = 3x2 - 6x - 9 y'' = 6x - 6 find the first and second derivatives 6x - 6 = 0 6x = 6 x = 1 [...]

14 08, 2015

## Tangents & Normals

By |2016-11-01T13:56:16+10:00August 14th, 2015||0 Comments

Tangents & Normals worked examples Show that the equation of the normal to the curve y = x3 - 5x at the point (1, -4) is given by x - 2y - 9 = 0 y' = 3x2 - 5 find the first derivative so we can get [...]

14 08, 2015

## First Principles

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

## Finding Values

By |2016-11-01T13:41:11+10:00August 14th, 2015||0 Comments

Finding Values worked examples Find the value of b if ƒ(x) = 5bx2 – 4x3 and ƒ''(–1) = –3. ƒ'(x) = 10bx - 12x2 find the first derivative remembering that b (or any letter that is not x) is to be considered just as a number ƒ''(x) = 10b [...]

14 08, 2015

## Surds & Fractions

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