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MathJax example

How would you determine the derivative of \((3x+5)^5\)?

At this stage you may try multiplying out the brackets and then differentiating. However, expanding \((3x+5)^5\) can be a bit challenging. In this section we will be looking at an alternative called the CHAIN RULE. The 2 formats we will be looking at are:

\({d \over dx}[f(x)]^n=n[f(x)]^{n-1}f^{'}(x)\)

\({d\over dx}f[g(x)]=f'[g(x)]g^{'}(x)\)

TRY THIS

Determine \({dy\over dx}\) for each of the following:

  1. \((x^3+4)^5\)
  2. \((4x^5+2)^3\)
  3. \((5x+x^2)^{-{2\over3}}\)
  4. \(\sqrt{x^4-9x}\)

SHOW SOLUTION

  1. \(15x^2(x^3+4)^4\)
  2. \(60x^4(4x^5+2)^2\)
  3. \(-{2\over3}(5+2x)(5x+x^2)^{-{5\over3}}\)
  4. \({1\over2}(4x^3-9)(x^4-9x)^{-{1\over2}}\)
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  • HOME
    • ABOUT
    • CONTACT ME
    • STUDENTS' SAY
  • FREE RESOURCES
    • HARRISON COLLEGE >
      • FIRST FORM
      • SECOND FORM
      • THIRD FORM
    • CSEC GENERAL MATHEMATICS
    • CSEC ADDITIONAL MATHEMATICS
    • CAPE UNIT 1
    • CAPE UNIT 2
  • COURSES
    • HARRISON COLLEGE >
      • FIRST FORM
      • SECOND FORM
      • THIRD FORM
      • FOURTH FORM
    • CSEC GENERAL MATHEMATICS
    • ADDITIONAL MATHEMATICS
    • CAPE UNIT 1 >
      • EXAM PREP
    • CAPE UNIT 2 >
      • EXAM PREP
  • NOTES
    • The Quadratic Formula
    • Third Form Notes