Question

Rule of derivatives:

y = 3x + 7 √x

Answer 1

rewrite using indices

\[y = 3x + 7x^{\frac{1}{2}}\]

now you can differentiate

Answer 2

Where does the 1/2 come from?

Answer 3

well the square root... the index law is

\[\sqrt{x} = x^{\frac{1}{2}}\]

or in general the nth root is

\[\sqrt[n]{x} = x^{\frac{1}{n}}\]

where n is an positive integer