Two variables, $x$ and $y$, are related by the equation $e^{2y} = 7x^4 + 2$. Given that \

Question

Two variables, $x$ and $y$, are related by the equation $e^{2y} = 7x^4 + 2$. Given that $y$ is decreasing at a rate of $\frac{2}{3}$ units per second when $x = 1$, find the rate of change of $x$ at this instant.

Accepted Answer

$\frac{dx}{dt}=-\frac{3}{7}\text{ units s}^{-1}$ (so $x$ is decreasing)

Differentiation - Connected Rates of Change

Differentiation - Connected Rates of Change

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