Given the function y=-2(-5x^(2)-2x)^(3), find (dy)/(dx) in any form. Answer: (dy)/(dx)=

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Given the function  y=-2(-5x^(2)-2x)^(3), find  (dy)/(dx) in any form. Answer:  (dy)/(dx)=

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Apply Chain Rule: First, we need to apply the chain rule to differentiate the function y = -2(-5x^2 - 2x)^3 with respect to x. 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 Functions: Let's identify the outer function and the inner function. The outer function is u^3 (where u is some function of x), and the inner function is u = -5x^2 - 2x. We will first differentiate the outer function with respect to u, which gives us 3u^2.Differentiate Outer Function: Now we differentiate the inner function u = -5x^2 - 2x with respect to x. The derivative of -5x^2 with respect to x is -10x, and the derivative of -2x with respect to x is -2. So the derivative of the inner function is du/dx = -10x - 2.Differentiate Inner Function: Next, we apply the chain rule by multiplying the derivative of the outer function with respect to u (which is 3u^2) by the derivative of the inner function with respect to x (which is -10x - 2). This gives us (dy/dx) = 3u^2 * (-10x - 2).Apply Chain Rule Multiplication: Substitute the inner function u back into the expression for u^2 to get (3(-5x^2 - 2x)^2) * (-10x - 2).Substitute Inner Function: Finally, we need to multiply the constant factor -2 from the original function y = -2(-5x^2 - 2x)^3 by the derivative we found. This gives us (dy/dx) = -2 * (3(-5x^2 - 2x)^2) * (-10x - 2).Multiply by Constant Factor: Simplify the expression to get the final derivative. (dy/dx) = -2 * 3 * (-10x - 2) * (-5x^2 - 2x)^2 = -6 * (-10x - 2) * (-5x^2 - 2x)^2.

Given the function $y=-2\left(-5 x^{2}-2 x\right)^{3}$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$

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Given the function y=−2(−5x2−2x)3 y=-2\left(-5 x^{2}-2 x\right)^{3} y=−2(−5x2−2x)3, find dydx \frac{d y}{d x} dxdy​ in any form.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

Given the function $y=-2\left(-5 x^{2}-2 x\right)^{3}$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$