Use implicit differentiation to find $y^{'}$ and then evaluate $y^{'}$ at the point $(2, 7)$ .
$y - 7 x^{3} + 7 = 0$
$\begin{array}{l} y^{'} = ◻ \\ {y^{'} |}_{(2, 7)} = ◻ (Simplify your answer.) \end{array}$

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So, the final answers are $y^{'} = - 21 x^{2}$ and $y^{'} |_{(2, 7)} = - 84$ .

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Step 1 ：Differentiate the given equation implicitly with respect to x. This means we will treat y as a function of x and use the chain rule when differentiating y. The derivative is $y^{'} = - 21 x^{2}$ .

Step 2 ：Substitute the point (2,7) into the derivative to find the slope of the tangent line at that point. The value of the derivative at the point (2,7) is $y^{'} |_{(2, 7)} = - 84$ .

Step 3 ：So, the final answers are $y^{'} = - 21 x^{2}$ and $y^{'} |_{(2, 7)} = - 84$ .

Use implicit differentiation to find y′ and then evaluate y′ at the point (2,7).y−7x3+7=0y′=◻y′|(2,7)=◻ (Simplify your answer.)

Answer

Popular Problems

Use implicit differentiation to find $y^{'}$ and then evaluate $y^{'}$ at the point $(2, 7)$ .
$y - 7 x^{3} + 7 = 0$
$\begin{array}{l} y^{'} = ◻ \\ {y^{'} |}_{(2, 7)} = ◻ (Simplify your answer.) \end{array}$