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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).