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

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

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Apply Chain Rule: Let's start by applying the chain rule to differentiate the function y=2^(-3x^(6)). 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. First, we identify the outer function as f(u) = 2^u and the inner function as u(x) = -3x^6. We will need to use the fact that the derivative of 2^u with respect to u is 2^u * ln(2).Differentiate Outer Function: Now we differentiate the outer function f(u) = 2^u with respect to u. f'(u) = 2^u * ln(2)Differentiate Inner Function: Next, we differentiate the inner function u(x) = -3x^6 with respect to x. u'(x) = d/dx(-3x^6) = -18x^5Apply Chain Rule Multiplication: We now apply the chain rule by multiplying the derivative of the outer function by the derivative of the inner function. y' = f'(u) * u'(x) = (2^(-3x^6) * ln(2)) * (-18x^5)Simplify Final Derivative: Simplify the expression to get the final derivative. y' = -18x^5 * 2^(-3x^6) * ln(2)

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

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Find the derivative of the following function.\newliney=2−3x6 y=2^{-3 x^{6}} y=2−3x6\newlineAnswer: y′= y^{\prime}= y′=

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