use implicit differentiation of the equation below to determine the slope of the graph at the…

use implicit differentiation of the equation below to determine the slope of the graph at the given\n\nxy^{4}=-49;x = -\\frac{1}{49},y = -7\n\nuse implicit differentiation to determine \\frac{dy}{dx}.\n\n\\frac{dy}{dx}=-\\frac{y}{4x}\n\nthe slope of the graph at the given point is \\square (simplify your answer)

use implicit differentiation of the equation below to determine the slope of the graph at the given\n\nxy^{4}=-49;x = -\\frac{1}{49},y = -7\n\nuse implicit differentiation to determine \\frac{dy}{dx}.\n\n\\frac{dy}{dx}=-\\frac{y}{4x}\n\nthe slope of the graph at the given point is \\square (simplify your answer)

Answer

Explanation:

Step1: Substitute values into derivative formula

Given (\frac{dy}{dx}=-\frac{y}{4x}), substitute (x =-\frac{1}{49}) and (y=-7) into the formula.

Step2: Calculate the slope

[ \begin{align*} \frac{dy}{dx}&=-\frac{-7}{4\times(-\frac{1}{49})}\ &=-\frac{-7}{-\frac{4}{49}}\ &=-\left(7\times\frac{49}{4}\right)\ &=-\frac{343}{4} \end{align*} ]

Answer:

(-\frac{343}{4})