Find the derivative of the following function. y=ln(8x^(3)) Answer: y^(')=

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Find the derivative of the following function.  y=ln(8x^(3)) Answer:  y^(')=

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Identify Function: Identify the function to differentiate. We have y = ln(8x^(3)). We need to find the derivative of y with respect to x, denoted as y'.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. Here, the outer function is ln(u) and the inner function is u = 8x^(3).Differentiate Outer Function: Differentiate the outer function. The derivative of ln(u) with respect to u is 1/u. So, if y = ln(u), then y' = 1/u * du/dx.Differentiate Inner Function: Differentiate the inner function. The inner function is u = 8x^(3). The derivative of 8x^(3) with respect to x is 24x^(2), since d/dx[x^(n)] = n*x^(n-1) and here n=3.Apply Chain Rule: Apply the derivatives from Steps 3 and 4 using the chain rule. We have y' = 1/u * du/dx, where u = 8x^(3) and du/dx = 24x^(2). Therefore, y' = 1/(8x^(3)) * 24x^(2).Simplify Expression: Simplify the expression for y'. y' = 1/(8x^(3)) * 24x^(2) simplifies to y' = 24x^(2)/(8x^(3)). We can cancel out x^(2) from the numerator and denominator and simplify the constants.Final Simplification: Final simplification. After canceling x^(2) and simplifying the constants, we get y' = 24/(8x). The constant 24/8 simplifies to 3, so y' = 3/x.

Find the derivative of the following function. $\newline$ $y=\ln \left(8 x^{3}\right)$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=ln⁡(8x3) y=\ln \left(8 x^{3}\right) y=ln(8x3)\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=\ln \left(8 x^{3}\right)$ $\newline$ Answer: $y^{\prime}=$