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This might seem like an obvious question and the instinctive urge is to disregard it entirely. Perhaps you would think "well that's silly, it's just not!"

Well, that's the intention of th...

1/2 e^x (sin x -cos x)

Firstly, the quadratic formula finds the roots of a quadratic equation. 
So this means f(x) = 0. A general polynomial with highest power 2 looks like: ax² + bx +c.
Usings the two fa...

look for common factors but there are not any in this case, it is a quadratic with 3 terms therefore it can be factorised into 2 brackets. First we look at the first term, since 7 is a prime number you ca...

You should write a^x as (e^lna)^x = e^xlna . ln(a) is a constant, so use the chain rule to differentiate this: lna(e^xlna) = lna(a^x)