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

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

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Identify Function: Identify the function to differentiate. We are given the function y = ln(x^6 - 6x^5). We need to find its derivative with respect to x.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 ln(u) and the inner function is u = x^6 - 6x^5.Differentiate Outer Function: Differentiate the outer function. The derivative of ln(u) with respect to u is 1/u. So, the derivative of the outer function evaluated at the inner function is 1/(x^6 - 6x^5).Differentiate Inner Function: Differentiate the inner function. The inner function is u = x^6 - 6x^5. Using the power rule, the derivative of x^6 is 6x^5, and the derivative of -6x^5 is -30x^4. So, the derivative of the inner function is 6x^5 - 30x^4.Multiply Derivatives: Multiply the derivatives of the outer and inner functions. Using the chain rule from Step 2, we multiply the derivative of the outer function by the derivative of the inner function to get the derivative of the composite function. This gives us (1/(x^6 - 6x^5)) * (6x^5 - 30x^4).Simplify Expression: Simplify the expression. We can simplify the expression by distributing the multiplication across the terms in the parentheses. This gives us (6x^5/(x^6 - 6x^5)) - (30x^4/(x^6 - 6x^5)).Factor Out Common Term: Factor out the common term in the numerator. We notice that x^4 is a common term in both numerators, so we can factor it out to simplify the expression further. This gives us x^4(6x - 30)/(x^6 - 6x^5).Cancel Common Factor: Cancel out the common factor of x in the numerator and denominator. We can cancel out one x from the term 6x in the numerator and one x from the x^5 in the denominator to simplify the expression to x^4(6 - 30)/(x^5 - 6x^4).Final Answer: Simplify the expression further. We can simplify the expression by combining the terms in the numerator, which gives us -24x^4/(x^5 - 6x^4).Write the final answer. The derivative of the function y = ln(x^6 - 6x^5) with respect to x is y' = -24x^4/(x^5 - 6x^4).

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

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Find the derivative of the following function.\newliney=ln⁡(x6−6x5) y=\ln \left(x^{6}-6 x^{5}\right) y=ln(x6−6x5)\newlineAnswer: y′= y^{\prime}= y′=

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