# Tutor profile: Jaeyoung K.

## Questions

### Subject: Basic Chemistry

What is an ion?

An ion, simply put, is an atom that has a positive or a negative electrical charge, due to the presence of an unequal number of negatively charged electrons and positively charged protons in its structure. If an ion has a net positive charge, it would be a cation, and if it has a net negative charge, it would be an anion.

### Subject: Biology

What is the role of the promoter sequence?

When DNA is transcribed into messenger RNA (mRNA), the RNA polymerase enzyme responsible for transcription will bind to a specific sequence to initiate the process. This sequence is the promoter sequence. Once the RNA polymerase binds to this sequence, it can transcribe the DNA sequence downstream from the promoter sequence into mRNA. It is important to keep in mind that oftentimes, this explanation is very much simplified - the binding of the RNA polymerase is also dependent in many cases on other conditions being met as well, such as the presence of the appropriate transcription factors.

### Subject: Calculus

Differentiate $$h(x) = \frac{6x^2}{ln 8x}$$

First, we need to find the derivatives of the numerator and the denominator: For the numerator: $$\frac{d}{dx} \ 6x^2 = 12x$$. We got this using $$\frac{d}{dx} \ mx^n = mnx^{n-1}$$ where m and n are constants. For the denominator: $$\frac{d}{dx} \ ln \ 8x = 1/x$$. We got this using $$\frac{d}{dx} ln x= 1/x$$ and the chain rule, $$\frac{d}{dx} f(g(x)) = f'(g(x)*g'(x)$$. In this case, $$f(g(x) = ln \ 8x$$, and $$g'(x) = 8$$ Now applying the quotient rule and plugging in the derivatives we found, we get $$h'(x) = \frac{(12x * ln \ 8x) - 6x}{(ln \ 8x)^2}$$. Remember that the quotient rule states: $$h(x) = \frac{a(x)}{b(x)}$$ then $$h'(x) = \frac{a'(x)*b(x) - a(x)*b'(x)}{(b(x))^2}$$