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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...

Here we have a product of two functions - they are being multiplied together - so we need to use the product rule. The product rule is: if y = u·v, dy/dx = v·u' + u·v' (where f' stands for df/dx). u = x^4...