Find the derivative of the following function. y=ln(5x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=ln(5x^(2)) Answer:  y^(')=

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Identify Function: Identify the function to differentiate. The function given is y = ln(5x^(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. In this case, the outer function is ln(u) and the inner function is u = 5x^(2).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.Differentiate Inner Function: Differentiate the inner function. The inner function is u = 5x^(2). The derivative of 5x^(2) with respect to x is 10x, because we use the power rule which states that the derivative of x^n is n*x^(n-1).Apply Chain Rule: Apply the chain rule. Using the chain rule, the derivative of y with respect to x is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. This gives us y' = (1/u) * (du/dx).Substitute and Simplify: Substitute u with 5x^(2) and du/dx with 10x. Substituting the expressions for u and du/dx into the chain rule formula, we get y' = (1/(5x^(2))) * (10x).Simplify Expression: Simplify the expression. Simplifying the expression for y', we get y' = 10x / (5x^(2)). We can simplify this further by canceling out an x from the numerator and denominator, which gives us y' = 10 / (5x).Simplify Constant: Simplify the constant. Simplifying the constant 10/5, we get y' = 2/x.

Find the derivative of the following function. $\newline$ $y=\ln \left(5 x^{2}\right)$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=ln⁡(5x2) y=\ln \left(5 x^{2}\right) y=ln(5x2)\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=\ln \left(5 x^{2}\right)$ $\newline$ Answer: $y^{\prime}=$