differentiate implicitly to find \\( \\frac { d y } { d x } \\)\n\n\\( y ^ { 8 } = x ^ { 7 } \\)\n\n\\(…

differentiate implicitly to find \\( \\frac { d y } { d x } \\)\n\n\\( y ^ { 8 } = x ^ { 7 } \\)\n\n\\( \\frac { d y } { d x } = \\)

differentiate implicitly to find \\( \\frac { d y } { d x } \\)\n\n\\( y ^ { 8 } = x ^ { 7 } \\)\n\n\\( \\frac { d y } { d x } = \\)

Answer

Explanation:

Step1: Differentiate both sides with respect to (x)

Differentiate (y^{8}) using the chain rule (\frac{d}{dx}(y^{8}) = 8y^{7}\frac{dy}{dx}), and differentiate (x^{7}) using the power rule (\frac{d}{dx}(x^{7})=7x^{6}). So we have (8y^{7}\frac{dy}{dx}=7x^{6}).

Step2: Solve for (\frac{dy}{dx})

Divide both sides of the equation (8y^{7}\frac{dy}{dx}=7x^{6}) by (8y^{7}). We get (\frac{dy}{dx}=\frac{7x^{6}}{8y^{7}}).

Answer:

(\frac{7x^{6}}{8y^{7}})