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Algebra
Question

Error Analysis. Below is the solution (possibly, with errors) for the derivative of the given function $$f ( x ) = \sqrt { 3 x - 7 }$$ using the differentiation formulas. Which of the following step(s) is/are the error(s) in the solution?

i. $$f ^ { \prime } ( x ) = \frac { 1 } { 2 } ( 3 x - 7 ) ^ { \frac { 1 } { 2 } - 1 } ( 3 )$$

ii. $$f ^ { \prime } ( x ) = \frac { 3 } { 2 } ( 3 x - 7 ) ^ { \frac { 1 } { 2 } }$$

iii. $$f ^ { \prime } ( x ) = \frac { 3 } { 2 \sqrt { 3 x - 7 } }$$