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

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

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Identify Function and Derivative: Identify the function and the type of derivative to be found. We are given the function y=log_6(-x^5) and we need to find its derivative with respect to x.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. In this case, the outer function is log_6(u) and the inner function is u=-x^5.Find Derivative of Outer Function: Find the derivative of the outer function. The derivative of log_6(u) with respect to u is 1/(u*ln(6)) because the derivative of log_b(u) is 1/(u*ln(b)).Find Derivative of Inner Function: Find the derivative of the inner function. The derivative of -x^5 with respect to x is -5x^4.Apply Chain Rule with Derivatives: Apply the chain rule using the derivatives from steps 3 and 4. The derivative of y with respect to x is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. So, y' = (1/(-x^5*ln(6)))*(-5x^4).Simplify Expression: Simplify the expression. y' = -5x^4 / (-x^5*ln(6)). We can simplify this by canceling out an x^4 from the numerator and denominator. y' = -5 / (-x*ln(6)).Cancel Negative Signs: Simplify further by canceling out the negative signs. y' = 5 / (x*ln(6)).

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

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