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the basic idea is to get everything with the unknown (let's assume this is x) on one side of the equals and everything else on the other side. To do this we use the 'inverse idea' to move our items onto d...

A special rule, the chain rule, exists for differentiating a function of another function (finding dy/dx).

Consider the expression cos x² . We call such an expression a ‘function of a fu...

√75 = 5√3, therefore 

x√48 = √75 + 3√3

x√48 = 5√3 + 3√3

x(√16 x √3) = 5√3 + 3√3

4x√3 = 5√3 + 3√3

4x√3 = (5 + 3)√3

4x√3 = 8√3

x√3 = 2√3

x = 2

Product rule:      dy/dx = uv' + u'v dy/dx = 2x(3x + 1) + x^2(3) dy/dx = 2x(3x + 1) +3x^2 dy/dx = 6x^2 + 2x + 3x^2 dy/dx = 9x^2 + 2x dy/dx = x(9x + 2)

There are two ways to prove they intercept (you can choose whichever one you prefer). Say we have two straight lines, for example: r₁ = 3i + 4...