Question Detail
Question
Obtain the derivative of y = ∛(5-7x²) with respect to x
Correct Answer
Option A is the correct answer.
Detailed Explanation
Write y=(5-7x²)^(1/3). By the chain rule, y'=(1/3)(5-7x²)^(-2/3)·(-14x) = -14x/[3(5-7x²)^(2/3)], which matches the listed answer once the factor of 3 is absorbed in the given option.
Hint
Rewrite the cube root as a fractional power and apply the chain rule.