Find the derivative of the following function. y=e^(-3x^(3)-7x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=e^(-3x^(3)-7x^(2)) Answer:  y^(')=

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Identify function: Identify the function to differentiate. The function given is y = e^(-3x^3 - 7x^2). We need to find the derivative of this function with respect to x.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 = -3x^3 - 7x^2.Differentiate outer function: Differentiate the outer function with respect to the inner function u. The derivative of e^u with respect to u is e^u. So, the derivative of the outer function is e^(-3x^3 - 7x^2).Differentiate inner function: Differentiate the inner function u = -3x^3 - 7x^2 with respect to x. The derivative of -3x^3 with respect to x is -9x^2, and the derivative of -7x^2 with respect to x is -14x. Therefore, the derivative of the inner function is -9x^2 - 14x.Apply chain rule multiplication: Apply the chain rule by multiplying the derivative of the outer function by the derivative of the inner function. The derivative of the outer function is e^(-3x^3 - 7x^2), and the derivative of the inner function is -9x^2 - 14x. Multiplying these together gives us the derivative of y with respect to x. y' = e^(-3x^3 - 7x^2) * (-9x^2 - 14x)Simplify derivative: Simplify the expression for the derivative. y' = -9x^2 * e^(-3x^3 - 7x^2) - 14x * e^(-3x^3 - 7x^2) This is the final form of the derivative.

Find the derivative of the following function. $\newline$ $y=e^{-3 x^{3}-7 x^{2}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=e−3x3−7x2 y=e^{-3 x^{3}-7 x^{2}} y=e−3x3−7x2\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=e^{-3 x^{3}-7 x^{2}}$ $\newline$ Answer: $y^{\prime}=$