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given that the chain rule is d/dx(f(g(x))) = g'(x)f'(g(x))given that the product rule is d/dx(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)given that the quotient rule is d/dx(f(x)/g(x)) = (g(x)f'(x) - g'(x)f(x))/(g(...

For a curve of f(x) against x, we can take the general point (x, f(x)) on the curve. By moving horizontally along the x-axis a distance of h, we also have the point (x+h, f(x+h)) on the curve. The gradien...

A stationary point is where the curve has 0 gradient. So to prove that x=4 is a stationary point, we must find the equation of the first derivative. To do this, differentiate x² - 2x - 24sqrtx....

Initially we find the first derivative of the function y = x⁶ + sqrt(x). We achieve this by multiplying each x term by the power it is raised to, then reducing the power by 1. Solution:<...

Well in a binomial expansion we need to remember the formula (1+x)^n = 1 + nx + (n(n-1)(x^2))/2! + (n(n-1)(n-2)x^3)/3! + ... (I can draw this out properly on the whiteboard app)There is another formula bu...