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# 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

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

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

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

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

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

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