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A) 4(cosec²(2x)) - (cosec²(x)) = 4/(sin²(2x)) - 1/(sin²(x)) = 4/[(2 sin(x) cos(x))²] - 1/(sin²(x)) B) 4/[(2 sin(x) cos(x))²] - ...

As we are given the derivative of f(x), we first need to integrate this derivative to obtain the function, f(x). Using the standard integration formula, ∫ x^n dx = (1/n+1)(x^(n+1)) +c, integrate each term...

Here, we use integration by parts. We must imagine ln(x) as a product of 1 and ln(x). We usually take the function of x to be our dv/dx, however, in the case of ln(x), we take that to be u (it is a specia...

This problem uses the binomial expansion formula: (x+y)ⁿ= _k=0Zⁿ _nC_k x^k y^n-k.But lets try to understand where this formula comes...

1. Explain the product rule: d/dx ( f(x) . g(x) ) = f'(x).g(x) = g'(x) . f (x)
   2. Briefly run through trigonometric derivatives.* cos (x) differentiates to: -sin(...