Given the function y=2(-7x^(2)-2x)^(6), find (dy)/(dx) in any form. Answer: (dy)/(dx)=

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Given the function  y=2(-7x^(2)-2x)^(6), find  (dy)/(dx) in any form. Answer:  (dy)/(dx)=

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Identify Function: We are given the function y=2(-7x^(2)-2x)^(6) and we need to find its derivative with respect to x, which is denoted as (dy)/(dx). To do this, we will use the chain rule, which 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. The outer function in this case is u^6 and the inner function is u=2(-7x^(2)-2x). Let's start by finding the derivative of the outer function with respect to its inner function u.Derivative of Outer Function: The derivative of u^6 with respect to u is 6u^(5). Now we will apply this to our function by substituting u with 2(-7x^(2)-2x), which gives us 6[2(-7x^(2)-2x)]^(5).Derivative of Inner Function: Next, we need to find the derivative of the inner function u=2(-7x^(2)-2x) with respect to x. The derivative of -7x^(2) with respect to x is -14x, and the derivative of -2x with respect to x is -2. Therefore, the derivative of the inner function with respect to x is 2(-14x - 2).Multiply Derivatives: Now we multiply the derivative of the outer function by the derivative of the inner function to get the overall derivative. This gives us (dy)/(dx) = 6[2(-7x^(2)-2x)]^(5) * 2(-14x - 2).Simplify Expression: We can simplify this expression by multiplying the constants outside the brackets. This gives us (dy)/(dx) = 12 * 6(-7x^(2)-2x)^(5) * (-14x - 2).Final Derivative: Finally, we multiply the constants 12 and 6 to get 72. So the derivative of the function y with respect to x is (dy)/(dx) = 72(-7x^(2)-2x)^(5) * (-14x - 2).

Given the function $y=2\left(-7 x^{2}-2 x\right)^{6}$ , 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(−7x2−2x)6 y=2\left(-7 x^{2}-2 x\right)^{6} y=2(−7x2−2x)6, find dydx \frac{d y}{d x} dxdy​ in any form.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

Given the function $y=2\left(-7 x^{2}-2 x\right)^{6}$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$