Given the function f(x)=-2(-8x^(2)-2)^(4), find f^(')(x) in any form. Answer: f^(')(x)=

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Given the function  f(x)=-2(-8x^(2)-2)^(4), find  f^(')(x) in any form. Answer:  f^(')(x)=

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Identify Functions: We are given the function f(x)=-2(-8x^(2)-2)^(4). To find the derivative f'(x), 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.Derivative of Outer Function: First, let's identify the outer function and the inner function. The outer function is u^4 where u is the inner function, and the inner function is -8x^2 - 2.Derivative of Inner Function: The derivative of the outer function u^4 with respect to u is 4u^3. We will later substitute the inner function back into u.Apply Chain Rule: The derivative of the inner function -8x^2 - 2 with respect to x is -16x, since the derivative of -8x^2 is -16x and the derivative of a constant is 0.Multiply by Constant: Now, we apply the chain rule: f'(x) = derivative of outer function evaluated at inner function times derivative of inner function. This gives us f'(x) = 4*(-8x^2 - 2)^3 * (-16x).Simplify Expression: Finally, we multiply the constant -2 from the original function by the derivative we just found to get the complete derivative of f(x). This gives us f'(x) = -2 * 4*(-8x^2 - 2)^3 * (-16x).Final Derivative: Simplify the expression by combining constants and keeping the rest of the expression intact. This gives us f'(x) = -2 * 4 * (-16x) * (-8x^2 - 2)^3.Multiplying the constants -2, 4, and -16x together, we get f'(x) = 128x * (-8x^2 - 2)^3.

Given the function $f(x)=-2\left(-8 x^{2}-2\right)^{4}$ , find $f^{\prime}(x)$ in any form. $\newline$ Answer: $f^{\prime}(x)=$

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Given the function f(x)=−2(−8x2−2)4 f(x)=-2\left(-8 x^{2}-2\right)^{4} f(x)=−2(−8x2−2)4, find f′(x) f^{\prime}(x) f′(x) in any form.\newlineAnswer: f′(x)= f^{\prime}(x)= f′(x)=

Given the function $f(x)=-2\left(-8 x^{2}-2\right)^{4}$ , find $f^{\prime}(x)$ in any form. $\newline$ Answer: $f^{\prime}(x)=$