Find the derivative of the following function. y=ln(2x^(3)-9x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=ln(2x^(3)-9x^(2)) Answer:  y^(')=

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Identify Function: Identify the function to differentiate. We have y = ln(2x^3 - 9x^2). We need to find the derivative of this function 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. Here, the outer function is ln(u) and the inner function is u = 2x^3 - 9x^2.Differentiate Outer Function: Differentiate the outer function. The derivative of ln(u) with respect to u is 1/u. So, the derivative of y with respect to u is 1/(2x^3 - 9x^2).Differentiate Inner Function: Differentiate the inner function. The inner function is u = 2x^3 - 9x^2. The derivative of u with respect to x is u' = d/dx(2x^3) - d/dx(9x^2) = 6x^2 - 18x.Apply Chain Rule: Apply the chain rule. Now we multiply the derivative of the outer function by the derivative of the inner function to get the derivative of y with respect to x. y' = (1/(2x^3 - 9x^2)) * (6x^2 - 18x).Simplify Expression: Simplify the expression. We can simplify the expression by distributing the multiplication. y' = (6x^2 - 18x) / (2x^3 - 9x^2).Factor Out Common Terms: Factor out common terms if possible. In this case, we can factor out an x from both the numerator and the denominator. y' = (6x(x - 3)) / (2x^2(x - 9/2)).Simplify Further: Simplify the expression further. We can cancel out an x from the numerator and denominator, and also simplify the constant in the denominator. y' = (6(x - 3)) / (2x(x - 9/2)). y' = (6(x - 3)) / (x(4x - 9)).

Find the derivative of the following function. $\newline$ $y=\ln \left(2 x^{3}-9 x^{2}\right)$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=ln⁡(2x3−9x2) y=\ln \left(2 x^{3}-9 x^{2}\right) y=ln(2x3−9x2)\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=\ln \left(2 x^{3}-9 x^{2}\right)$ $\newline$ Answer: $y^{\prime}=$