Find the derivative of the following function. y=8^(9x^(5)-5x^(4)) Answer: y^(')=

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Find the derivative of the following function.  y=8^(9x^(5)-5x^(4)) Answer:  y^(')=

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Identify Function Components: Identify the function and its components. We have y = 8^(9x^(5) - 5x^(4)). This is an exponential function with a base of 8 and an exponent of 9x^5 - 5x^4.Apply Chain Rule: Apply the chain rule for derivatives. 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. Here, the outer function is a(u) = 8^u and the inner function is u(x) = 9x^5 - 5x^4.Derivative of Outer Function: Find the derivative of the outer function a(u) = 8^u with respect to u. The derivative of a^u with respect to u is a^u * ln(a), where a is a constant and u is the variable. So, a'(u) = 8^u * ln(8).Derivative of Inner Function: Find the derivative of the inner function u(x) = 9x^5 - 5x^4 with respect to x. The derivative of 9x^5 with respect to x is 45x^4, and the derivative of -5x^4 with respect to x is -20x^3. So, u'(x) = 45x^4 - 20x^3.Apply Chain Rule with Derivatives: Apply the chain rule using the derivatives from steps 3 and 4. y' = a'(u) * u'(x) y' = (8^(9x^5 - 5x^4) * ln(8)) * (45x^4 - 20x^3)Simplify Derivative: Simplify the expression for the derivative. y' = 8^(9x^5 - 5x^4) * ln(8) * (45x^4 - 20x^3) This is the final form of the derivative.

Find the derivative of the following function. $\newline$ $y=8^{9 x^{5}-5 x^{4}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function. $\newline$ $y=8^{9 x^{5}-5 x^{4}}$ $\newline$ Answer: $y^{\prime}=$