Find the derivative of the following function. y=ln(4x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=ln(4x^(2)) Answer:  y^(')=

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Identify function: Identify the function to differentiate. We have y = ln(4x^(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 = 4x^(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, where u = 4x^(2).Differentiate inner function: Differentiate the inner function with respect to x. The inner function is u = 4x^(2). The derivative of 4x^(2) with respect to x is 8x. So, d/dx[4x^(2)] = 8x.Apply chain rule: Apply the chain rule using the derivatives from steps 3 and 4. The derivative of y with respect to x is the derivative of the outer function times the derivative of the inner function. So, y' = (1/u) * (8x), where u = 4x^(2).Substitute back: Substitute u back into the derivative. Replace u with 4x^(2) in the expression for y'. y' = (1/(4x^(2))) * (8x).Simplify expression: Simplify the expression. y' = 8x / (4x^(2)). We can simplify this by canceling out an x from the numerator and denominator. y' = 8 / (4x).Simplify constant: Simplify the constant. Divide 8 by 4 to get 2. y' = 2 / x.

Find the derivative of the following function. $\newline$ $y=\ln \left(4 x^{2}\right)$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=ln⁡(4x2) y=\ln \left(4 x^{2}\right) y=ln(4x2)\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=\ln \left(4 x^{2}\right)$ $\newline$ Answer: $y^{\prime}=$