Find the derivative of the following function. y=ln(-7x^(3)-6x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=ln(-7x^(3)-6x^(2)) Answer:  y^(')=

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Identify function: Identify the function to differentiate. We have y = ln(-7x^3 - 6x^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 = -7x^3 - 6x^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, the derivative of the outer function is 1/(-7x^3 - 6x^2).Differentiate inner function: Differentiate the inner function with respect to x. The inner function is u = -7x^3 - 6x^2. The derivative of -7x^3 with respect to x is -21x^2, and the derivative of -6x^2 with respect to x is -12x. So, the derivative of the inner function is -21x^2 - 12x.Apply chain rule: Apply the chain rule to find the derivative of the composite function. Using the chain rule, the derivative of y with respect to x is (1/(-7x^3 - 6x^2)) * (-21x^2 - 12x).Simplify expression: Simplify the expression. We multiply the two derivatives together to get the final derivative: y' = (1/(-7x^3 - 6x^2)) * (-21x^2 - 12x) = (-21x^2 - 12x) / (-7x^3 - 6x^2).

Find the derivative of the following function. $\newline$ $y=\ln \left(-7 x^{3}-6 x^{2}\right)$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=ln⁡(−7x3−6x2) y=\ln \left(-7 x^{3}-6 x^{2}\right) y=ln(−7x3−6x2)\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=\ln \left(-7 x^{3}-6 x^{2}\right)$ $\newline$ Answer: $y^{\prime}=$