For the following equation, find f^(')(x). f(x)=-7x^(5)+7x^(3)-9x^(2)-9x-8 Answer: f^(')(x)=

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For the following equation, find  f^(')(x).  f(x)=-7x^(5)+7x^(3)-9x^(2)-9x-8 Answer:  f^(')(x)=

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Apply Power Rule: To find the derivative of the function f(x) = -7x^(5) + 7x^(3) - 9x^(2) - 9x - 8, we will apply the power rule to each term separately. The power rule states that the derivative of x^n with respect to x is n*x^(n-1).Derivative of -7x^(5): First, we find the derivative of the term -7x^(5). Using the power rule, we get: (d)/(dx)(-7x^(5)) = -7 * 5 * x^(5-1) = -35x^(4).Derivative of 7x^(3): Next, we find the derivative of the term 7x^(3). Using the power rule, we get: (d)/(dx)(7x^(3)) = 7 * 3 * x^(3-1) = 21x^(2).Derivative of -9x^(2): Then, we find the derivative of the term -9x^(2). Using the power rule, we get: (d)/(dx)(-9x^(2)) = -9 * 2 * x^(2-1) = -18x.Derivative of -9x: After that, we find the derivative of the term -9x. Since this is a linear term, its derivative is simply the coefficient: (d)/(dx)(-9x) = -9.Derivative of Constant Term: Lastly, the derivative of a constant term like -8 is 0, since constants do not change and therefore their rate of change is zero: (d)/(dx)(-8) = 0.Combine Derivatives: Now, we combine all the derivatives we found to get the derivative of the entire function f(x): f^(')(x) = -35x^(4) + 21x^(2) - 18x - 9.

For the following equation, find $f^{\prime}(x)$ . $\newline$ $f(x)=-7 x^{5}+7 x^{3}-9 x^{2}-9 x-8$ $\newline$ Answer: $f^{\prime}(x)=$

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For the following equation, find f′(x) f^{\prime}(x) f′(x).\newlinef(x)=−7x5+7x3−9x2−9x−8 f(x)=-7 x^{5}+7 x^{3}-9 x^{2}-9 x-8 f(x)=−7x5+7x3−9x2−9x−8\newlineAnswer: f′(x)= f^{\prime}(x)= f′(x)=

For the following equation, find $f^{\prime}(x)$ . $\newline$ $f(x)=-7 x^{5}+7 x^{3}-9 x^{2}-9 x-8$ $\newline$ Answer: $f^{\prime}(x)=$