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

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

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Identify Function Type and Rule: Identify the type of function and the rule needed to find its derivative. The function y = 6^(9x^(6)+8x^(5)) is an exponential function with a variable exponent. To differentiate it, we need to use the chain rule and the fact that the derivative of a^u with respect to x is a^u * ln(a) * u', where u is a function of x.Apply Chain Rule: Apply the chain rule to differentiate the function. Let u = 9x^(6) + 8x^(5). Then y = 6^u. The derivative of y with respect to x is dy/dx = d(6^u)/dx = 6^u * ln(6) * du/dx.Find u Derivative: Find the derivative of u with respect to x. We have u = 9x^(6) + 8x^(5). The derivative of u with respect to x is du/dx = d(9x^(6))/dx + d(8x^(5))/dx = 54x^(5) + 40x^(4).Substitute into dy/dx: Substitute the derivative of u into the derivative of y. Now we can substitute du/dx into the expression for dy/dx from Step 2. We get dy/dx = 6^(9x^(6)+8x^(5)) * ln(6) * (54x^(5) + 40x^(4)).Simplify if Necessary: Simplify the expression if necessary. The expression for the derivative is already in its simplest form, so no further simplification is needed.

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

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