Tutor profile: Kalila M.

Find the derivative of $$ (x^3 + x^2 + x) (lnx) $$

To find the derivate of the above equation, use the Product Rule: $$ d/dx f(x)g(x) = f'(x)g(x) + f(x)g'(x) $$ So first find the derivative of the first bracket: $$ d/dx (x^3 + x^2 + x) (lnx) $$ $$ = (3x^2 + 2x + 1) (lnx) + (x^3 + x^2 + x) d/dx (lnx) $$ Now use the rule that $$ d/dx (lnx) = 1/x $$ $$ = (3x^2 + 2x + 1) (lnx) + (x^3 + x^2 + x) (1/x) $$ We can simplify by multiplying the brackets of the second term: $$ = (3x^2 + 2x + 1) (lnx) + (x^2 + x + 1) $$

Explain why the cross-price elasticity of substitutes will be positive and the cross-price of complements will be negative.

The cross-price elasticity measures the degree of change in demand for one good with the change in another good's price. Substitutes are goods where the consumer can substitute one for the other, for example, branded or generic medication. For example, if the price of branded medication increases, then consumers may switch to generic medication, meaning the demand for generic medication increases and so the cross-price elasticity of demand is positive. Complements on the other hand are goods that the consumer purchases together, one example could be fuel and vehicles. Here the cross-price elasticity of demand is negative, because if the price of fuel increases, then the demand for vehicles may decrease.

Find the mistake in the following answer: 2x - 6 = 12 2x = 12 - 6 2x = 6 x = 3

The mistake is in the second step, where the solution required us to add rather than subtract 6 from both sides. The correct solution is: 2x - 6 = 12 2x = 12 + 6 2x = 18 x = 9 With algebraic equations, we can always check our answer by plugging it back into the original equation, so: 2(9) - 6 = 18 - 6 = 12