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

Identify Function Components: Identify the function and its components. We have y = ln(x^6 - 8x^5). The function inside the natural logarithm is u(x) = x^6 - 8x^5.Find Inner Function Derivative: Find the derivative of the inner function u(x) = x^6 - 8x^5. Using the power rule, we differentiate term by term. u'(x) = d/dx(x^6) - d/dx(8x^5) u'(x) = 6x^5 - 40x^4Apply Chain Rule: Apply the chain rule to differentiate y = ln(u(x)). The chain rule states that if y = ln(u(x)), then y' = u'(x)/u(x). We already found u'(x) in Step 2, and u(x) is given by the inner function. y' = (6x^5 - 40x^4) / (x^6 - 8x^5)

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Find the derivative of the following function.

y=ln(x^(6)-8x^(5))
Answer:
y^(')=

Find the derivative of the following function. $\newline$ $y=\ln \left(x^{6}-8 x^{5}\right)$ $\newline$ Answer: $y^{\prime}=$

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Q. Find the derivative of the following function.

\newline

y=\ln \left(x^{6}-8 x^{5}\right)

\newline

Answer:

y^{\prime}=

Identify Function Components: Identify the function and its components. $\newline$ We have $y = \ln(x^6 - 8x^5)$ . The function inside the natural logarithm is $u(x) = x^6 - 8x^5$ .
Find Inner Function Derivative: Find the derivative of the inner function $u(x) = x^6 - 8x^5$ . Using the power rule, we differentiate term by term. $u'(x) = \frac{d}{dx}(x^6) - \frac{d}{dx}(8x^5)$ $u'(x) = 6x^5 - 40x^4$
Apply Chain Rule: Apply the chain rule to differentiate $y = \ln(u(x))$ . The chain rule states that if $y = \ln(u(x))$ , then $y' = \frac{u'(x)}{u(x)}$ . We already found $u'(x)$ in Step $2$ , and $u(x)$ is given by the inner function. $y' = \frac{6x^5 - 40x^4}{x^6 - 8x^5}$