Differentiating using First Principals. To find the gradient of a tangent at the point A Equation of the tangent takes the form y = mx +c m is the gradient.

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Presentation transcript:

Differentiating using First Principals

To find the gradient of a tangent at the point A Equation of the tangent takes the form y = mx +c m is the gradient of the tangent

1. Start with a chord of length AB 2. B moves towards A. 3. When B reaches C the chord is getting shorter and closer to A

Gradient AB = x f(x) h x+h f(x+h) A B

Example: Find the gradient of the tangent at any point x

Substituting

Example: Find the gradient of the tangent at any point x Multiply out the brackets

Example: Find the gradient of the tangent at any point x Divide top and bottom by h

Example: Find the gradient of the tangent at any point x h becomes 0

Note: Differentiated gives

Practice: Differentiate from first principals:

Worksheet 1