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To answer this question we need to first decide what the question is asking for. In this case the question is asking for the first and second differential of a given function. If we have a function f(x) =...

Using the chain rule of dy/dx=dy/du * du/dx we label sin(x) as u. Now we differentiate u with respect to x, getting cos(x). Then we differentiate u² , getting 2u. Mutiplying these together gets...

We start with: 2ln6 - ln3 ... First, we rewrite this expression as: ln6 + ln6 - ln3 ... Next, we rewrite this as: ln(23) + ln(23) - ln3 ... Using the log rule log_axy = log_ax...

The first step in scoring full marks on this typically 4 mark question is to recognise what it's asking you to do. We use the process of differentiation to solve it. f(x)=2x^3 - 2x^2 + 8xf'(x) = 6x^2 - 4x...

We need to split the initial fraction into two. We know that (x-5)/(x+1)(x-2) is equivalent to A/(x+1) + B/(x-2). Multiplying by (x+1)(x-2) we get x-5 = A(x-2) + B(x+1). Expanding the brackets gives x - 5...