find the derivative of the following equation: a) y = 5x^3 - 4x^-4 + xb

Ans: dy/dx = 15x^2 + 16x^-5 + b To solve for the first part of the right hand side, remember to bring the power of 3 forward and multiply, then reduce our power by 1 to leave 15x^2. For the second part, be careful to notice the two negative signs and note that (-4)^2 will equal positive 16. Then, as before, bring the power down by 1 and be careful again to notice the negative sign to avoid any mistakes using -3 instead of -5. Lastly, it is important to remember to include our constant, b. The power of x has reduced from 1 to 0 but this does not mean our b disappears. Careless mistakes here will cost valuable marks in the exam.