Given the function y=-3(4x^(2)-9x)^(4), find (dy)/(dx) in any form. Answer: (dy)/(dx)=

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Given the function  y=-3(4x^(2)-9x)^(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 = -3(4x^2 - 9x)^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.Identify Outer and Inner Functions: First, let's identify the outer function and the inner function. The outer function is u^4 (where u is a function of x), and the inner function is u = 4x^2 - 9x. We will need to take the derivative of the outer function with respect to u and then multiply it by the derivative of the inner function with respect to x.Derivative of Outer Function: The derivative of the outer function u^4 with respect to u is 4u^3. So, if we apply this to our function, we get the derivative of -3(4x^2 - 9x)^4 with respect to the inner function (4x^2 - 9x) as -3 * 4(4x^2 - 9x)^3.Derivative of Inner Function: Now, we need to find the derivative of the inner function 4x^2 - 9x with respect to x. The derivative of 4x^2 with respect to x is 8x, and the derivative of -9x with respect to x is -9. So, the derivative of the inner function with respect to x is 8x - 9.Combine Derivatives: We can now combine the derivatives of the outer and inner functions. The derivative of y with respect to x is the derivative of the outer function times the derivative of the inner function, which is -3 * 4(4x^2 - 9x)^3 * (8x - 9).Simplify Expression: Simplify the expression by multiplying the constants and combining like terms. The derivative of y with respect to x is -12(4x^2 - 9x)^3 * (8x - 9).

Given the function $y=-3\left(4 x^{2}-9 x\right)^{4}$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$

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Given the function y=−3(4x2−9x)4 y=-3\left(4 x^{2}-9 x\right)^{4} y=−3(4x2−9x)4, find dydx \frac{d y}{d x} dxdy​ in any form.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

Given the function $y=-3\left(4 x^{2}-9 x\right)^{4}$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$