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22461278
Differentiation
Description
My first mind map. Identifies key concepts of derivatives
No tags specified
differentiation
gradient
derivative
mathematics
as level
Mind Map by
ken dekpor
, updated more than 1 year ago
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Created by
Vivienne Holmes
almost 8 years ago
Copied by
ken dekpor
almost 4 years ago
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Resource summary
Differentiation
Attachments:
Differentiation quiz
Why? To find the gradient of a curve at a point
Equivalent to finding the gradient of the tangent to the curve at that point
Gradient of equation is change in y divided by change in x
Annotations:
y-y1=m(x-x1) m=(y-y1) /(x-x1)
Gradient of normal is the negative inverse of m or negative inverse dy/dx
Annotations:
y=x3 at x =1, y=1 dy/dx = 3x^2 so at x=1, gradient = 3. Normal = - 1/m So at x=1, y=1 gradient = -1/3
Gradient of a tangent= dy/dx
Annotations:
y=x3 at x =1, y=1 dy/dx = 3x^2 so at x=1, gradient = 3.
A gradient is the rate of change
How to differentiate?
Differentiating a polynomial function (one variable)
Attachments:
Differenting polynomials
Chain Rule
Attachments:
Chain Rule Slides
Product Rule
Attachments:
Product Rule
Quotient Rule
Attachments:
Quotient Rule
Natural Logarithm and Exponential functions
Attachments:
Natural Log Function
Natural exponential function
Trig Functions
Attachments:
Trig functions
The gradient of a function has different names
The gradient function
The derived function with respect to x
The differential coefficient with respect to x
The first differential with respect to x
dy/dx
f'(x)
Differentiate dy/dx to get the second order differential
The second order differential has different names
d^2y/dx^2
f''(x)
The second derivative of a function
How to find maximum and minimum values of the function
At maximum and minimum values of f(x), f'(x) = 0.
At maximum value, f''(x) is negative
At minimum value, f''(x) is positive
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