Dr. J's Maths.com
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Calculus - Differentiation - the Product Rule.
Test Yourself 1.


 

Differentiate each of the following equations using the Product Rule with respect to the relevant pronumeral:

No rule. 1. y = 3x4 (2x - 5) 2.
One bracket. 3. y = x (2x + 4)4 4. s = t3 (3t + 1)3
  5. y = (4 - 3x)5 x4 6. V = (1 - 2r)3 4r
Two brackets - could expand but do as product rule for practice. 7. y = (2x + 3)2(x - 4) 8. m = (n3 + 5)2(4n - 1)
Two brackets - higher power - proper Product Rule:) 9. y = (x + 3)(x - 2)5 10. V = (4 - r)(1 - 2r)3
  11. Given that f(x) = (x+1)(x-1)5,

find the values of a and b such that

f '(x) = (ax+b)(x-1)4.

   y = x4(x + 1)3
Two brackets - both with powers. 11. y = (2x - 1)3 (x - 3)2 12. D = (x + 1)3 (x + 2)2
Surds. 13. 14.