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There are two ways you can take the derivative of a^x.

1) 

Let y = a^x    now we're trying to find dy/dx

2)

ln(y) = xln(a)    take logs of both s...

Generally you will be asked to find the root of an equation of the form F(x) = 0. In my answer below I will only touch on graphical methods, but will go into deeper detail on showing that a root lays in a...

Step 1 - Identify the difference between the required form of the answer and the expression to be simplified: 

It can be...

(7+√5)/(√5-1) 

In this example we are given (√5-1) as our denominator, and we want to simplify this complex fraction into the form a + b√5. 

In order to do this our first st...

Easy! We first consider which number is in the square root. Then we look at it's factors:- if any of factors are square we can immediately take their root out of the overall square root. Once all the squa...