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Introduction to Differentiation Math Review

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What is differentiation? Definition of a derivative.

Differentiation is the process of finding the derivative f'(x) of a function f.  It is a part of maths called Calculus

 

The derivative is the gradient of the tangent of the graph of f at the point x.


Definition of a derivative

 

Differentiation examples

f(x) = x³   f'(x) = 3x²
f(x) = 2x²   f'(x) = 2 x 2x = 4x
f(x) = 7x³   f'(x) = 7 x 3x² = 21x²

 

 

When an expression has several terms, find the derivative of each term separately.  You may need to expand brackets first.

f(x) = 3x³ + 2x²   f'(x) = 9x² + 4x

 

 

Note:

  • The derivative of x is 1.
  • The derivative of any number (e.g. 1) is 0.

The derivative of a function

 

Differentiation problems for you to try.

Differentiate:
Differentiation problems

 

Differentiation answers