Find the derivative of the following function. y=e^(-6x^(2)-9x) Answer: y^(')=

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Find the derivative of the following function.  y=e^(-6x^(2)-9x) Answer:  y^(')=

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Identify function: Identify the function to differentiate. y = e^(-6x^2 - 9x)Recognize composition: Recognize that this is a composition of functions: the exponential function and the inner function -6x^2 - 9x.Apply chain rule: Apply the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.Calculate outer function derivative: Calculate the derivative of the outer function, e^u, where u = -6x^2 - 9x. The derivative of e^u with respect to u is e^u. (dy/du) = e^uCalculate inner function derivative: Calculate the derivative of the inner function, u = -6x^2 - 9x, with respect to x. (du/dx) = d/dx(-6x^2 - 9x) = -12x - 9Combine derivatives: Combine the derivatives using the chain rule. (dy/dx) = (dy/du) * (du/dx) (dy/dx) = e^(-6x^2 - 9x) * (-12x - 9)Simplify final derivative: Simplify the expression to get the final derivative. y' = -e^(-6x^2 - 9x) * (12x + 9)

Find the derivative of the following function. $\newline$ $y=e^{-6 x^{2}-9 x}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=e−6x2−9x y=e^{-6 x^{2}-9 x} y=e−6x2−9x\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=e^{-6 x^{2}-9 x}$ $\newline$ Answer: $y^{\prime}=$