Science:Math Exam Resources/Courses/MATH110/April 2017/Question 01 (e)

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MATH110 April 2017

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Question 01 (e)
Find the derivative of $y={\frac {1+x^{2}}{3x}}$ . .

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Noticing there are two terms adding in numerator and one term in denominator, split $y$ into two parts and then calculate derivative separately for two simple parts.

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Solution
$y={\frac {1+x^{2}}{3x}}$ Split it into two parts $y={\frac {1}{3x}}+{\frac {x}{3}}$ Using the sum rule of derivative, $(f+g)'=f'+g'$ for all functions f and g. calculate derivative for two parts $y'=({\frac {1}{3x}})'+({\frac {x}{3}})'$ $y'={\frac {1}{3}}(x^{-1})'+{\frac {1}{3}}1$ $y'={\frac {1}{3}}(-x^{-2})+{\frac {1}{3}}$ $y'=-{\frac {1}{3x^{2}}}+{\frac {1}{3}}$ answer:* $\color {blue}-{\frac {1}{3x^{2}}}+{\frac {1}{3}}$