Find the derivative of the following function. y=8^(-9x^(5)+6x^(4)) Answer: y^(')=

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Find the derivative of the following function.  y=8^(-9x^(5)+6x^(4)) Answer:  y^(')=

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Identify Function Components: Identify the function and its components. We have y = 8^(-9x^(5) + 6x^(4)). This is an exponential function with a base of 8 and an exponent of -9x^5 + 6x^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 + 6x^4.Derivative of Outer Function: Find the derivative of the outer function a(u) with respect to u. The derivative of a^u with respect to u is a^u * ln(a), where a is a constant. So, a'(u) = 8^u * ln(8).Derivative of Inner Function: Find the derivative of the inner function u(x) with respect to x. The inner function is u(x) = -9x^5 + 6x^4. Using the power rule, the derivative is u'(x) = d/dx(-9x^5) + d/dx(6x^4) = -45x^4 + 24x^3.Apply Chain Rule with Derivatives: Apply the chain rule using the derivatives from steps 3 and 4. The chain rule gives us y'(x) = a'(u(x)) * u'(x). Substitute a'(u) and u'(x) into the equation. y'(x) = (8^(-9x^5 + 6x^4) * ln(8)) * (-45x^4 + 24x^3).Simplify Derivative: Simplify the expression for the derivative. y'(x) = 8^(-9x^5 + 6x^4) * ln(8) * (-45x^4 + 24x^3). This is the simplified form of the derivative.

Find the derivative of the following function. $\newline$ $y=8^{-9 x^{5}+6 x^{4}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=8−9x5+6x4 y=8^{-9 x^{5}+6 x^{4}} y=8−9x5+6x4\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=8^{-9 x^{5}+6 x^{4}}$ $\newline$ Answer: $y^{\prime}=$