Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Calculus - Differentiation - Basic techniques.
Test Yourself 2.


 

Find the gradient function of the following functions - that is "differentiate each of the following functions" with respect to the given variable. All questions use only the direct technique as described - no special rules.

As always - your first step is to look at the structure and decide what you need to do.

The questions below focus on the structures of:
1. the basic format.
2. the use of simple brackets.
3. the use of the d/dx format.
4. radicals.
5. terms in the denominator.
6. fractions with only one term in the denominator.

 

Basic format 1. 2. 3.
  4. 5. 6.
  7. y = |x| 8. . 9.
Simple brackets 10. 11. 12.
  13.    
  16.    
Use of the d/dx format. 19.    
  22.    
  25.    
Radicals 28. . 29. . 30.
  31.    
  34.    
Terms in the denominator. 37. . 38. .

39. (i) Express as a sum of two fractions.

(ii) Hence differentiate

.
  40.    
  43.    
Fractions with one term in the denominator. 46.    
  49.    
  52.