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Subsitute in u = 3x^2 + 6x and use chain rule to get dy/dx = dx/du x dy/dx to get dy/dx = 2(6x+6)e^(3x^2 +6)

a) We compare the expansion given to the standard binomial expansion (remembering the powers of k).(1+kx)ⁿ=1+n(kx)+(n(n-1)/2)(kx)²+...As this is true for all x (for which the expansi...

First, recall the Product rule: f(x)=g(x)*h(x), f'(x)=h(x)*g'(x)+h'(x)*g(x)This reveals the next step, to find the derivatives of our two subsidiary functions(g and h) d/dx * (sin4x) = 4cos(4x) , and d/dx...

The easiest way to solve this is to split the fraction into partials.Using partial fractions, we get A/(x-3)+B/x=x+3/(x(x-3)) implies Ax+B(x-3)=x+3We want to find the values of A and B that solve this, so...

The stationary points are located where the gradient of the function is equal to 0. The first derivative of the function describes the gradient so we must differentiate the function to find dy/dx.
U...