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This is a question that can be answered in two ways: using the product rule and the rule for differentiating powers, we will do both to see how the two rules are equivalent. chain rule: split the function...

Completing the square is often useful when solving equations! An example: x² +6x-7=0. Step 1) We want to move the constant to the right hand side: x²+6x=7. Step 2) Now, add the squar...

= (1/125) ^ 2/3  = (1/5) ^ 2 = 1/25 To find a number to a negative power, you invert it (flip it so that 125 becomes 1/125) To find (1/125) ^ 2/3, find the cube root of 1/125 (=1/5) and then square it (=1...

Here, f(x) and g(x) are functions of x, whose output depends on the value of x.

fg(2) means fg(x) where x=2.

Firstly, calculate g(2) and use this answer as the new value of x for f(x).

The first step here is to find a common factor in each term. If we first look at the coefficients of each term we can see the first common factor is 3, so we can write that first outside of our brackets. ...