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 a quadratic function. The outer function is e^u, and the inner function is u(x) = -6x^2 + 9x.Find derivative outer function: Find the derivative of the outer function with respect to u, where u = -6x^2 + 9x. If v = e^u, then v' = e^u * du/dx.Find derivative inner function: Find the derivative of the inner function u(x) = -6x^2 + 9x with respect to x. u'(x) = d/dx(-6x^2 + 9x) = d/dx(-6x^2) + d/dx(9x) = -12x + 9.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. y' = e^u * u'(x) where u = -6x^2 + 9x and u'(x) = -12x + 9.Substitute into derivative: Substitute u and u'(x) into the derivative of the outer function. y' = e^(-6x^2 + 9x) * (-12x + 9).Simplify final answer: Simplify the expression to get the final answer. y' = (-12x + 9)e^(-6x^2 + 9x).

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: $y^{\prime}=$