Use implicit differentiation to find the slope of the tangent line to the curve [ frac{y}{x-7 y}=x^{3}+7 ] at the point ( left(1, frac{8}{57} ight) ). slope ( = ) Submit Question
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Starting with the equation \(\frac{y}{x-7 y}=x^{3}+7\), we can rewrite it as \(y = x^{3}(x-7y) + 7(x-7y)\). Now, we can differentiate both sides with respect to \(x\): \(\frac{dy}{dx} = 3x^{2}(x-7y) + x^{3}\frac{d}{dx}(x-7y) + 7\frac{d}{dx}(x-7y)\). This Show more…
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