Given that y =2x^3 + 3/(x^2), find a) dy/dx and b) the integral of y
a) It is useful to rewrite the equation using power rules, so we get y = 2x3 + 3x-2Now we can simply use the differentiation rules where we multiply the coefficient (number before x) by the power, then reducing the power by one.This way we get dy/dx = 6x2 - 6x-3b) Once again it is simpler to integrate y = 2x3 + 3x-2We use the integration rules of increasing the power by one then dividing the coefficient by the new power:(2x4)/4 + (3x-1)/1 + c= (x4)/2 - 3x-1 + cRemember, as we are doing indefinite integration (integrating y but not between 2 limits), we must add a constant that we can call c.
BS
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