Calculus – Differentiation

 

Differentiation

 
 

Introducing the Rate of Change

 
  • What is the rate of change
  • Rate of change  vs.  Slope  vs.  Gradient

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From 1st principles

(not required for GCSE but a useful video for those student who would like a challenge)
 
  • What is.... from 1st principles
  • Derivative of a non-linear equation using 1st principles.
  • An example
 

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The Power Rule

 
  • What is the power rule
  • Finding the derivative of an equation using the power rule
  • Some examples of using the power rule
 

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Finding the equation of the Tangent Line at a point on the curve

 

Tangent Lines are linear of the form  y = mx + b

  • The derivative of the curve at point 'a' gives the slope 'm' of the tangent line at that point
  • With the coordiantes of our point 'a' and the slope 'm', use the slope formula

m = (y - y1)/(x - x1)

to workout the equation of the tangent line

 

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