139010
Description
Mind Map by bill.backster, updated more than 1 year ago
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Created by bill.backster
over 11 years ago
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Differentiation
- basic diff formulas
- chain Rule
- g[f(x)} = g'[f(x)]*f'(x)
- g[f(x)} = g'[f(x)]*f'(x)
- Product Rule
- f(x)*g(x) = f'(x)*g(x) + f(x)*g'(x)
- UV = U'V + UV'
- UV = U'V + UV'
- f(x)*g(x) = f'(x)*g(x) + f(x)*g'(x)
- Quotient Rule
- f(x)/g(x) = {f'(x)*g(x) - f(x)*g'(x)}/[g(x)]^2
- U/V = {U'V - UV'}/V^2
- U/V = {U'V - UV'}/V^2
- f(x)/g(x) = {f'(x)*g(x) - f(x)*g'(x)}/[g(x)]^2
- chain Rule
- Notation
- f'(x)
- dy/dx
- d/dx
- y'
- Dx{f(x)}
- f'(x)
- diff Rules
- Exponential and Logarithmic Functions
- trig functions
- second Derivitives
- f''(x)
- [d^2y] / [dx^2]
- To double diff simply diff your original
function and then diff it again to finf
the double diff.
- f''(x)
- Basic functions
- on graphs
- f'(x) = 0 stationary point
- nature of stationary points
- maximum when double diff < 0
- minimum when double diff > 0
- maximum when double diff < 0
- nature of stationary points
- f'(x) = 0 stationary point
- applications
- diff = 0 to find speed and velocity
- double diff to get the acceleration
- continuous - differentiable
- dis-continuous- non differentiable
- average rate of change = (y2-y1)/(x2-x1)
- diff = 0 to find speed and velocity
- tangents to curves
- gradient of tangent = diff at certain point.
- equation y=mx+c using gradient found above sub in points to find C
- equation of normal flip the gradient of tangent and use same method to find equation.
- equation of normal flip the gradient of tangent and use same method to find equation.
- equation y=mx+c using gradient found above sub in points to find C
- gradient of tangent = diff at certain point.
- Exponential and Logarithmic Functions
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