Use implicit differentiation to find $y^{\prime}$ for the equation below and then evaluate $y^{\prime}$ at the indicated point.
\[
y^{2}+3 y+4 x=0 ;(-1,1)
\]

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Answer

Final Answer: $\boxed{4}$

Steps

Step 1 ：Differentiate both sides of the equation with respect to x. This will involve using the chain rule on the left side of the equation, as y is a function of x.

Step 2 ：After differentiating, solve for y', which is the derivative of y with respect to x.

Step 3 ：Substitute the given point into the equation to find the value of y' at that point.

Step 4 ：The derivative of the function at the point (-1,1) is 4.

Step 5 ：Final Answer: $\boxed{4}$

Use implicit differentiation to find $y^{\prime}$ for the equation below and then evaluate $y^{\prime}$ at the indicated point.\[y^{2}+3 y+4 x=0 ;(-1,1)\]

Answer

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Use implicit differentiation to find $y^{\prime}$ for the equation below and then evaluate $y^{\prime}$ at the indicated point.
\[
y^{2}+3 y+4 x=0 ;(-1,1)
\]