Find the derivative of the following function. y=log_(3)(-7x^(6)-9x^(5)) Answer: y^(')=

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Find the derivative of the following function.  y=log_(3)(-7x^(6)-9x^(5)) Answer:  y^(')=

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Identify Function & Derivative Type: Identify the function and the type of derivative to be found. We need to find the derivative of the function y with respect to x, where y=log_(3)(-7x^(6)-9x^(5)). This is a logarithmic differentiation problem.Apply Chain Rule for Logarithmic Differentiation: Apply the chain rule for logarithmic 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. For a logarithm with base 3, the derivative of y=log_(3)(u) with respect to x is 1/(u * ln(3)) times the derivative of u with respect to x, where u is the inner function.Differentiate Inner Function: Differentiate the inner function u with respect to x. The inner function u is -7x^(6)-9x^(5). Using the power rule, the derivative of u with respect to x is u' = -7*6x^(6-1) - 9*5x^(5-1) = -42x^(5) - 45x^(4).Combine Results from Steps 2 & 3: Combine the results from Step 2 and Step 3. Using the chain rule from Step 2 and the derivative of the inner function from Step 3, we get y' = 1/((-7x^(6)-9x^(5)) * ln(3)) * (-42x^(5) - 45x^(4)).Simplify Derivative Expression: Simplify the expression for the derivative. We can factor out a common factor of x^4 from the numerator to simplify the expression. y' = x^4 * (-42x - 45) / ((-7x^(6)-9x^(5)) * ln(3)).Check for Further Simplifications: Check for any possible simplifications. There are no further simplifications that can be made without changing the form of the expression significantly. The final answer is y' = x^4 * (-42x - 45) / ((-7x^(6)-9x^(5)) * ln(3)).

Find the derivative of the following function. $\newline$ $y=\log _{3}\left(-7 x^{6}-9 x^{5}\right)$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=log⁡3(−7x6−9x5) y=\log _{3}\left(-7 x^{6}-9 x^{5}\right) y=log3​(−7x6−9x5)\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=\log _{3}\left(-7 x^{6}-9 x^{5}\right)$ $\newline$ Answer: $y^{\prime}=$