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

Logarithmic functions - Differentiation - basic techniques.
Test Yourself 1.


 

The questions on this page focus on differentiating:

  1. the basic structure;
  2. using the chain rule;
  3. using the product rule;
  4. using the quotient rule;
  5. using log laws;

Differentiate each of the following:
Basic structure 1. y = ln (3x-2) 2. y = loge(6x2 - 3)
  3. Find f '(e) if

.

 4. y = loge (1 - 3x2)
  5. y = loge 2ex 6. .
Chain rule 7. 8.
  9. y = [ln (2x - 1)]3 10. y = loge (loge ex)
Product rule 11. Show that the derivative of

x[(logex)2 - 2 logex + 2] = [logex]2
  12. y = x lnx 13. y = 4x2 ln (2 - x)
  14. y = 2x3 loge (3x - 7) 15. (x2 - 5)ln(3 - x2)
  16. Determine the range of values of x where the curve

y = x2 ln x is concave up.

 17. Determine the range of values for which the curve has a negative gradient.

Answer correct to 3 decimal places.

Answer.0 < x < 0.607.
Quotient rule 18. . 19.
  20. 21.
Use log laws 22. y = loge105x+2. 23. y = 7ln (4 - 2x)3
  24. y = 3ln [(2x - 1)(3x + 2)] 25. y = 10ln [(x + 3)2(5x - 2)3]
  26. 27.
  28. 29.
  30. y = log2x 31. y = x2 log2x a