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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 ...

Use the power rule on the right hand side of the equation to reduce the expression into simpler termsRemoves logs (several methods, I would personally halve and then cancel)Factorise to give x=a(4a^2<...