Differentiation

bill.backster
Mind Map by bill.backster, updated 11 months ago
bill.backster
Created by bill.backster over 6 years ago
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Mind Map on Differentiation, created by bill.backster on 06/25/2013.

Resource summary

Differentiation
1 basic diff formulas
1.1 chain Rule
1.1.1 g[f(x)} = g'[f(x)]*f'(x)
1.2 Product Rule
1.2.1 f(x)*g(x) = f'(x)*g(x) + f(x)*g'(x)
1.2.1.1 UV = U'V + UV'
1.3 Quotient Rule
1.3.1 f(x)/g(x) = {f'(x)*g(x) - f(x)*g'(x)}/[g(x)]^2
1.3.1.1 U/V = {U'V - UV'}/V^2
2 Notation
2.1 f'(x)
2.2 dy/dx
2.3 d/dx
2.4 y'
2.5 Dx{f(x)}
3 diff Rules
3.1 Exponential and Logarithmic Functions
3.2 trig functions
3.3 second Derivitives
3.3.1 f''(x)
3.3.2 [d^2y] / [dx^2]
3.3.3 To double diff simply diff your original function and then diff it again to finf the double diff.
3.4 Basic functions
3.5 on graphs
3.5.1 f'(x) = 0 stationary point
3.5.1.1 nature of stationary points
3.5.1.1.1 maximum when double diff < 0
3.5.1.1.2 minimum when double diff > 0
3.6 applications
3.6.1 diff = 0 to find speed and velocity
3.6.2 double diff to get the acceleration
3.6.3 continuous - differentiable
3.6.4 dis-continuous- non differentiable
3.6.5 average rate of change = (y2-y1)/(x2-x1)
3.7 tangents to curves
3.7.1 gradient of tangent = diff at certain point.
3.7.1.1 equation y=mx+c using gradient found above sub in points to find C
3.7.1.1.1 equation of normal flip the gradient of tangent and use same method to find equation.
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