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To prove n³-n is a multiple of 3 we rely on a few simple tricks. The first is to factorise the expression.n³-n = n(n²-1)n(n²-1) = (n-1)(n)(n+1)The next trick is...

Now remember that for differentiating polynomials the power is times by the coefficient and the power is reduced by one. This would mean that the answer now becomes: 2x + 2

Start by trying to find a common multiple of the last term, e.g. if you have a quadratic that ends in 4, when you factorise this function, we should get two terms ending in multiplies of 4 so (1,4) or (2,...

We use the product rule with u=x and v=ln(x) (so u'=1 andv'=1/x) to differentiate xln(x) to ln(x)+1, and -x just differentiates to -1, hence we have. f'(x)=ln(x).
Now note that ln(x^3)=3ln(x) using p...

First we can equate (19x - 2)/((5 - x)(1 + 6x)) to A/(5-x) + B/(1+6x) which means: (19x - 2)/((5 - x)(1 + 6x)) = A/(5-x) + B/(1+6x). Then we will turn the RHS into a single fraction: (19x - 2)/((5 - x)(1 ...