Given the function y=4(x^(2)+6x-6)^(4), find (dy)/(dx) in any form. Answer: (dy)/(dx)=

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Given the function  y=4(x^(2)+6x-6)^(4), find  (dy)/(dx) in any form. Answer:  (dy)/(dx)=

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Apply Chain Rule: To find the derivative of the function y = 4(x^2 + 6x - 6)^4 with respect to x, we will use the chain rule. 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 u^4 (where u = x^2 + 6x - 6) and the inner function is x^2 + 6x - 6.Differentiate Outer Function: First, we differentiate the outer function u^4 with respect to u. The derivative of u^4 is 4u^3.Differentiate Inner Function: Next, we differentiate the inner function x^2 + 6x - 6 with respect to x. The derivative of x^2 is 2x, the derivative of 6x is 6, and the derivative of -6 is 0. So, the derivative of the inner function is 2x + 6.Apply Chain Rule Again: Now, we apply the chain rule by multiplying the derivative of the outer function by the derivative of the inner function. This gives us: (dy/dx) = 4u^3 * (2x + 6).Substitute Back Expression: We substitute back the expression for u to get the derivative in terms of x. So, (dy/dx) = 4(x^2 + 6x - 6)^3 * (2x + 6).Simplify Final Derivative: Finally, we can simplify the expression by distributing the 4 into the expression (x^2 + 6x - 6)^3. This gives us the final derivative: (dy/dx) = 4 * (2x + 6) * (x^2 + 6x - 6)^3.

Given the function $y=4\left(x^{2}+6 x-6\right)^{4}$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$

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Given the function y=4(x2+6x−6)4 y=4\left(x^{2}+6 x-6\right)^{4} y=4(x2+6x−6)4, find dydx \frac{d y}{d x} dxdy​ in any form.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

Given the function $y=4\left(x^{2}+6 x-6\right)^{4}$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$