Find the derivative of the following function. y=2^(-8x^(5)+2x^(4)) Answer: y^(')=

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Find the derivative of the following function.  y=2^(-8x^(5)+2x^(4)) Answer:  y^(')=

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Identify Function Components: Identify the function and its components. We have the function y = 2^(-8x^(5) + 2x^(4)). This is an exponential function with a base of 2 and an exponent that is a polynomial in 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 2^u and the inner function is u = -8x^(5) + 2x^(4).Differentiate Outer Function: Differentiate the outer function with respect to the inner function u. The derivative of 2^u with respect to u is (2^u) * ln(2), where ln(2) is the natural logarithm of 2.Differentiate Inner Function: Differentiate the inner function u = -8x^(5) + 2x^(4) with respect to x. The derivative of -8x^(5) is -40x^(4), and the derivative of 2x^(4) is 8x^(3). So, the derivative of the inner function u with respect to x is u' = -40x^(4) + 8x^(3).Apply Chain Rule Multiplication: Apply the chain rule by multiplying the derivatives from Step 3 and Step 4. The derivative of y with respect to x is y' = (2^(-8x^(5) + 2x^(4))) * ln(2) * (-40x^(4) + 8x^(3)).Simplify Derivative Expression: Simplify the expression for the derivative. y' = (2^(-8x^(5) + 2x^(4))) * ln(2) * (-40x^(4) + 8x^(3)) can be left as is, or factored to show the common factor of 8x^(3). y' = 8x^(3) * (2^(-8x^(5) + 2x^(4))) * ln(2) * (-5x + 1)

Find the derivative of the following function. $\newline$ $y=2^{-8 x^{5}+2 x^{4}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=2−8x5+2x4 y=2^{-8 x^{5}+2 x^{4}} y=2−8x5+2x4\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=2^{-8 x^{5}+2 x^{4}}$ $\newline$ Answer: $y^{\prime}=$