Question

given the equation \\(x - y^9 = 2\\), find \\(\frac{dx}{dy}\\) by implicit differentiation.

Explanation:

Differentiate both sides with respect to y

$$ \frac{d}{dy}(x - y^9) = \frac{d}{dy}(2) $$

Apply differentiation rules

$$ \frac{dx}{dy} - 9y^8 = 0 $$

Solve for the derivative

$$ \frac{dx}{dy} = 9y^8 $$

Answer:

Given the equation \(x - y^9 = 2\), find \(\frac{dx}{dy}\) by implicit differentiation.

\(\frac{dx}{dy} =\) <blank>\(9y^8\)</blank>