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As the coefficient of x^2 is not 1, we think of this equation as ax^2 +bx + c. When the coefficient of x^2 is not 1, then we need to firstly multiply the first and last numbers together (8 and -3) which g...

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...