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(1+x)^3 = x^3 + 3x^2 + 3x + 1 (Can be calculated straight away by binomial method or by multiplying brackets individually)
if (1+x)^3 > 1 + 3x^2 + x^3then: x^3 + 3x^2 + 3x + 1 > 1 + 3x^2 +...

We want to find dy/dx. We find this using the product rule by setting the functions f(x) = x and g(x) = e^2x. With these functions, we can write the equation as y = f(x)g(x), so by applying the ...

answer may not be obvious at first, but by using intergration by parts, treating part 1 as lnx and part 2 as 1, you will get xlnx-1

(a) To differentiate implicitly, differentiate x’s as normal and differentiate y’s with respect to y before multiplying by dy/dx. Therefore the differentiating the curve gives
9x^(1/2) + 10y*(dy/dx) ...

Differentiate to get:dy/dx = 12x^3 -24x^2Factorise and set equal to 0:12x^2(x-2) = 0Solve to get x = 2 and x =0.