Find the derivative of the following function. y=e^(2x^(4)) Answer: y^(')=

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Find the derivative of the following function.  y=e^(2x^(4)) Answer:  y^(')=

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Identify Function: Identify the function and its components. The function y = e^(2x^(4)) is an exponential function where the exponent is a function of x itself, namely 2x^(4).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 = 2x^(4).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, (d/du)(e^u) = e^u.Differentiate Inner Function: Differentiate the inner function u = 2x^(4) with respect to x. Using the power rule, the derivative of 2x^(4) with respect to x is 8x^(3). So, (d/dx)(2x^(4)) = 8x^(3).Apply Chain Rule: Apply the chain rule using the derivatives from steps 3 and 4. The derivative of y with respect to x is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. Therefore, y' = e^(2x^(4)) * 8x^(3).Simplify Derivative: Simplify the expression for the derivative. y' = 8x^(3) * e^(2x^(4)).

Find the derivative of the following function. $\newline$ $y=e^{2 x^{4}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function. $\newline$ $y=e^{2 x^{4}}$ $\newline$ Answer: $y^{\prime}=$