y = 4x^3 - 5/x^2 find dy/dx

First rewrite the equation into an easier form:y = y = 4x^3 - 5x^-2dy/dx means differentiate y with respect to xSo when differentiating, you look at the first term and write the co-efficient of the x term ( so in this case the first term is 4x^3 and the co-efficient is 4) then bring down the value of the exponent and multiply it to the co-efficient (hence 3 is the exponent). Then decrease the value of the exponent by 1. Do this for all the terms in the equation. dy/dx = (4)(3)x^2 - (5)(-2)x^-3If we simplify this equation we get:dy/dx = 12x^2 +10x^-3 ( remember 2 negatives multiplied together give a positive)now lets put the equation back tothe form it was given in the question (i.e. with the fraction in the second term)dy/dx = 12x^2 +10/x^3