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y = x^x, by taking logs:ln(y) = ln(x^x )By log laws:ln(y) = xln(x)From implicit differentiation; d/dx = y'*d/dy, so:d/dx[ln(y)] = y'*d/dy[ln(y)] = y' * 1/yFrom the product rule; d/dx[...

Algebra is fundamentally the way in which we can find out the value of some unknown element. So for example, if a salesman agrees to sell two apples for £10 algebra can help us find out how much one apple...

4 x £15 = £60 2 x £10 = £20 This means the total price for tickets without added fees is £60 + £20 = £8010% booking fee --> £80 x 1.1 = £88 3% extra to pay with credit card --> £88 x 1.03 = £90.64 A...

There are two main steps. First find the gradient of the curve at x = 2 (m). This is done by differentiating the curve equation y = 3x^2 + 4 to get dy/dx = 6x. By plugging in x = 2, we get the gradient of...

First, we make the standard assumption that there is no air resistance, meaning that gravity is the only force acting on our cannonball. We then use the SUVAT equations, so: S = 0m (because it will return...