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

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

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Identify Functions: We are given the function y=e^(-2x^(6)). To find the derivative, we will use 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.Differentiate Outer Function: First, let's identify the outer function and the inner function. The outer function is e^(u) where u is the inner function, and the inner function is -2x^(6).Differentiate Inner Function: Now, we differentiate the outer function with respect to the inner function u. The derivative of e^(u) with respect to u is e^(u).Apply Chain Rule: Next, we differentiate the inner function -2x^(6) with respect to x. Using the power rule, the derivative of -2x^(6) is -12x^(5).Simplify Expression: Now, we apply the chain rule by multiplying the derivative of the outer function by the derivative of the inner function. This gives us the derivative of y with respect to x. y' = e^(-2x^(6)) * (-12x^(5))Simplify the expression to get the final answer. y' = -12x^(5)e^(-2x^(6))

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

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