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1. Explain the product rule: d/dx ( f(x) . g(x) ) = f'(x).g(x) = g'(x) . f (x)
   2. Briefly run through trigonometric derivatives.* cos (x) differentiates to: -sin(...

To rationalise a fraction we have to eliminate the surds in the denominator. We know we can multiply the top and the bottom of a fraction by the same thing, as this is equivalent to multiplying by 1. Noti...

First of all you calculate dy/dx. To do this you look at each x individually. For the first x you multiply it by it's power and then minus 1 from the power to get 3x^2. Then multiply the next x by the pow...

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)

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<...