Find the derivative of the following function. y=log_(4)(-9x^(4)-x^(3)) Answer: y^(')=

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Find the derivative of the following function.  y=log_(4)(-9x^(4)-x^(3)) Answer:  y^(')=

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Identify Function & Base: Identify the function and the base of the logarithm. We have the function y = log_4(-9x^4 - x^3), where the base of the logarithm is 4.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 log_4(u) and the inner function is u = -9x^4 - x^3.Differentiate Outer Function: Differentiate the outer function with respect to the inner function. The derivative of log_4(u) with respect to u is 1/(u * ln(4)), where ln is the natural logarithm.Differentiate Inner Function: Differentiate the inner function with respect to x. The inner function is u = -9x^4 - x^3. Its derivative with respect to x is du/dx = -36x^3 - 3x^2.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 dy/dx = (1/(-9x^4 - x^3 * ln(4))) * (-36x^3 - 3x^2).Simplify Expression: Simplify the expression. We can factor out -3x^2 from the numerator to get dy/dx = (-3x^2(12x + 1))/(ln(4)(-9x^4 - x^3)).Check for Simplifications: Check for any possible simplifications or cancellations. There are no further simplifications or cancellations that can be made without changing the domain of the original function.

Find the derivative of the following function. $\newline$ $y=\log _{4}\left(-9 x^{4}-x^{3}\right)$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=log⁡4(−9x4−x3) y=\log _{4}\left(-9 x^{4}-x^{3}\right) y=log4​(−9x4−x3)\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=\log _{4}\left(-9 x^{4}-x^{3}\right)$ $\newline$ Answer: $y^{\prime}=$