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because the equation is made up of two functions we can think of them separately when differentiating:f(x)= x^3 f'(x)= 3x^2g(x)= e^x g'(x)= e^xdy/dx= (3x^2e^x)+ (x^3e^x)

First of all we need to identify what it is we're trying to get onto one side of the equation. In this example;y = 2x - 5 we are asked to arrange the formula in terms of x. To do this we need to first get...

a) First, we need to factorize (x²+x-6) = (x-2)(x+3). Therefore, g(x) = x/(x+3) + 3(2x+1)/(x-2)(x+3) = x(x-2)/(x-2)(x+3) + 3(2x+1)/(x-2)(x+3) = (x²-2x + 6x +3)/(x-2)(x+3) = (x^2<...

Part A)Expand numerator in the integral to get 14x^(2) - 2xe^(-2x)-5Now divide by denominator to get 14x - 2e^(-2x) - 5/xNow integrate to get 7x^(2) + e^(-2x) - 5ln(x)Part B)Get all components of y on the...

This is a simultaneous equation question, and it is important to read the question and pick out the information we want, and see what we are trying to get to, then work out a pathway on how we will get to...