### Differential and Integral Calculus (21-120) — Feedback on Homework 5

Homework 5 was due on Thursday 26th September 2013 and consisted of:

• Section 3.6 Q 3, 9, 23, 39, 49

I marked Q 9, 23 and 39 (out of 3 each); a free mark was given for submitting the homework.

Section 3.6 Q9. This question was done well on the whole; the most common error was differentiating $\ln(5x)$ incorrectly, obtaining either $\frac{1}{5x}$ or $\frac{5}{x}$. In fact, the derivative of $\ln(5x)$ is just $\frac{1}{x}$.

Section 3.6 Q23. Most errors arising in this question were from people forgetting to apply the product rule and chain rule.

Section 3.6 Q39. People who did this question the intended way usually did it well. The question asked specifically that you should use logarithmic differentiation, in other words you start by writing $$\ln(y) = 2\ln(x^2+2) + 4\ln(x^4+4)$$ and proceed from there. Another common error was for people to get $4x$ instead of $4x^3$ as their derivative of $x^4$... be careful!

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