Find the derivative of the following function. y=ln(9x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=ln(9x^(2)) Answer:  y^(')=

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Identify function: Identify the function to differentiate. We have y = ln(9x^(2)). 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 = 9x^(2).Differentiate outer function: Differentiate the outer function with respect to the inner function. The derivative of ln(u) with respect to u is 1/u. So, d/dx[ln(u)] = 1/u * du/dx.Differentiate inner function: Differentiate the inner function with respect to x. The inner function is u = 9x^(2). The derivative of 9x^(2) with respect to x is 18x. So, du/dx = 18x.Substitute derivatives: Substitute the derivatives into the chain rule formula. We have d/dx[ln(u)] = 1/u * du/dx. Substituting the derivatives from steps 3 and 4, we get d/dx[ln(9x^(2))] = 1/(9x^(2)) * 18x.Simplify expression: Simplify the expression. Simplify the derivative to get y' = (18x)/(9x^(2)). This simplifies further to y' = 2/x.

Find the derivative of the following function. $\newline$ $y=\ln \left(9 x^{2}\right)$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=ln⁡(9x2) y=\ln \left(9 x^{2}\right) y=ln(9x2)\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=\ln \left(9 x^{2}\right)$ $\newline$ Answer: $y^{\prime}=$