Given the function f(x)=-5(5x^(2)+6x-8)^(5), find f^(')(x) in any form. Answer: f^(')(x)=

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Given the function  f(x)=-5(5x^(2)+6x-8)^(5), find  f^(')(x) in any form. Answer:  f^(')(x)=

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Identify Functions: To find the derivative of the function f(x) = -5(5x^(2) + 6x - 8)^(5), 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.Find Outer Function Derivative: First, let's identify the outer function and the inner function. The outer function is g(u) = -5u^(5) and the inner function is u(x) = 5x^(2) + 6x - 8. We will find the derivative of each function separately.Find Inner Function Derivative: The derivative of the outer function g(u) = -5u^(5) with respect to u is g'(u) = -5 * 5u^(5-1) = -25u^(4).Apply Chain Rule: The derivative of the inner function u(x) = 5x^(2) + 6x - 8 with respect to x is u'(x) = 2 * 5x + 6 = 10x + 6.Substitute Derivatives: Now, we apply the chain rule: f'(x) = g'(u(x)) * u'(x). Substituting the derivatives we found, we get f'(x) = (-25u^(4)) * (10x + 6).Replace Inner Function: We need to replace u with the inner function u(x) = 5x^(2) + 6x - 8 to express the derivative entirely in terms of x. So, f'(x) = -25(5x^(2) + 6x - 8)^(4) * (10x + 6).Simplify Expression: Finally, we simplify the expression by distributing the -25: f'(x) = -25 * (10x + 6) * (5x^(2) + 6x - 8)^(4).

Given the function $f(x)=-5\left(5 x^{2}+6 x-8\right)^{5}$ , find $f^{\prime}(x)$ in any form. $\newline$ Answer: $f^{\prime}(x)=$

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Given the function f(x)=−5(5x2+6x−8)5 f(x)=-5\left(5 x^{2}+6 x-8\right)^{5} f(x)=−5(5x2+6x−8)5, find f′(x) f^{\prime}(x) f′(x) in any form.\newlineAnswer: f′(x)= f^{\prime}(x)= f′(x)=

Given the function $f(x)=-5\left(5 x^{2}+6 x-8\right)^{5}$ , find $f^{\prime}(x)$ in any form. $\newline$ Answer: $f^{\prime}(x)=$