Science:Math Exam Resources/Courses/MATH110/December 2012/Question 03 (c)

MATH110 December 2012

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Question 03 (c)
Calculate the following derivative. You may leave your answer unsimplified. $\displaystyle f'(x)$, where $f(x)={\dfrac {e^{3x}}{3x}}$.

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
You need to use the quotient rule and one other rule to calculate this derivative.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. To begin calculating this derivative, apply the quotient rule. So $f'(x)={\frac {(e^{3x})'*(3x)-e^{3x}*(3x)'}{(3x)^{2}}}$ The derivative of 3x is simple to calculate, but in order to calculate $(e^{3x})'$ we will need to use the chain rule as follows: $\displaystyle (e^{3x})'=e^{3x}*(3x)'=e^{3x}*3$ Plugging this back into the quotient rule, we get: $f'(x)={\frac {(e^{3x}*3)*(3x)-e^{3x}*(3)}{(3x)^{2}}}$ You can leave this answer as is.

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