Question

given the equation \\(x^8 + y^5 = 25\\), find \\(\frac{dy}{dx}\\) by implicit differentiation.

answer

\\(\frac{dy}{dx} =\\)

Explanation:

Differentiate both sides with respect to x

$$ \frac{d}{dx}(x^8 + y^5) = \frac{d}{dx}(25) $$

$$ 8x^7 + 5y^4 \frac{dy}{dx} = 0 $$

Solve for dy/dx

$$ 5y^4 \frac{dy}{dx} = -8x^7 $$

$$ \frac{dy}{dx} = -\frac{8x^7}{5y^4} $$

Answer:

Given the equation \(x^8 + y^5 = 25\), find \(\frac{dy}{dx}\) by implicit differentiation.

Answer

\(\frac{dy}{dx} =\) <blank>\(-\frac{8x^7}{5y^4}\)</blank>