# Tutor profile: Tiana R.

## Questions

### Subject: Calculus

What is the derivative of $$ f(x) = 3x^2 - x $$

Use the power rule for each expression then add the two: $$ \frac{\partial {ax^b}}{\partial{x}} = a \times b x^{b-1}$$ $$ \frac{\partial {3x^2}}{\partial{x}} = 3 \times 2 x^{2-1} = 6x$$ $$ \frac{\partial {-x}}{\partial{x}} = -x^{1-1} = -1$$ $$ \frac{\partial {(3x^2 - x)}}{\partial{x}} = 6x - 1$$

### Subject: Economics

How can countries gain from international trade?

When countries voluntarily engage in international trade, they can always achieve mutual benefits. First, if a country can produce two goods A and B. If this country specializes in the production of good A because it is more productive at producing good A than B, then this country will able to generate more good A and can export the surplus to other countries and then import good B from another country. Second, resources are finite so a country can also specialize in the production of a good that uses abundant resources as opposed to goods that require less abundant and scarcer resources.

### Subject: Statistics

If $$P(A) = 0.4, P(B) = 0.3, A \cap B = \emptyset. P(A \cup B) = 0.7.$$ True or False

Recall that $$P(A \cup B) = P(A) + P(B) - P(A \cap B) $$. Given that the intersection of A and B is empty, $$P(A \cap B)=0$$, hence $$P(A \cup B) = P(A) + P(B) = 0.4 + 0.3 = 0.7$$. This statement is True.

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