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For the following equation, evaluate (dy)/(dx) when x=-3. y=3x^(2)+3 Answer:

For the following equation, evaluate dydx \frac{d y}{d x} when x=−3 x=-3 .\newliney=3x2+3 y=3 x^{2}+3 \newlineAnswer:

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Full solution

Q. For the following equation, evaluate dydx \frac{d y}{d x} when x=−3 x=-3 .\newliney=3x2+3 y=3 x^{2}+3 \newlineAnswer:
  1. Evaluate Derivative at x=−3x = -3: Now that we have the derivative dydx=6x\frac{dy}{dx} = 6x, we need to evaluate it at x=−3x = -3. Substitute x=−3x = -3 into the derivative to get dydx=6(−3)\frac{dy}{dx} = 6(-3). Calculate the value: dydx=6(−3)=−18\frac{dy}{dx} = 6(-3) = -18.
  2. Substitute x=−3x = -3: We have found the value of dydx\frac{dy}{dx} when x=−3x = -3, which is −18-18. There are no further calculations needed, so we can conclude the solution.

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