Find the derivative of the following function. y=e^(-6x^(3)+5x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=e^(-6x^(3)+5x^(2)) Answer:  y^(')=

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Identify function: Identify the function to differentiate. y = e^(-6x^(3) + 5x^(2)) We need to find the derivative of y with respect to x, denoted as y'.Apply chain rule: Apply the chain rule for differentiation. The chain rule 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. In this case, the outer function is e^u and the inner function is u = -6x^(3) + 5x^(2).Differentiate outer function: Differentiate the outer function with respect to the inner function u. If y = e^u, then the derivative of y with respect to u is dy/du = e^u.Differentiate inner function: Differentiate the inner function u with respect to x. u = -6x^(3) + 5x^(2) The derivative of u with respect to x is du/dx = d/dx(-6x^(3)) + d/dx(5x^(2)) du/dx = -18x^(2) + 10xApply chain rule: Apply the chain rule by multiplying the derivatives from Step 3 and Step 4. y' = dy/du * du/dx y' = e^(-6x^(3) + 5x^(2)) * (-18x^(2) + 10x)

Find the derivative of the following function. $\newline$ $y=e^{-6 x^{3}+5 x^{2}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=e−6x3+5x2 y=e^{-6 x^{3}+5 x^{2}} y=e−6x3+5x2\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=e^{-6 x^{3}+5 x^{2}}$ $\newline$ Answer: $y^{\prime}=$