For the following equation, find f^(')(x). f(x)=-6x^(5)-9x^(4)+x^(3)+6 Answer: f^(')(x)=

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For the following equation, find  f^(')(x).  f(x)=-6x^(5)-9x^(4)+x^(3)+6 Answer:  f^(')(x)=

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Apply Power Rule: To find the derivative of the function f(x) = -6x^(5) - 9x^(4) + x^(3) + 6, 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 -6x^(5): First, we find the derivative of the term -6x^(5). Using the power rule, we get: (d)/(dx)(-6x^(5)) = -6 * 5 * x^(5-1) = -30x^(4).Derivative of -9x^(4): Next, we find the derivative of the term -9x^(4). Again, using the power rule, we get: (d)/(dx)(-9x^(4)) = -9 * 4 * x^(4-1) = -36x^(3).Derivative of x^(3): Then, we find the derivative of the term x^(3). Using the power rule, we get: (d)/(dx)(x^(3)) = 3 * x^(3-1) = 3x^(2).Derivative of constant: Finally, the derivative of a constant is zero, so the derivative of the term +6 is: (d)/(dx)(6) = 0.Combine all derivatives: Now, we combine the derivatives of all terms to find the derivative of the entire function f(x): f^(')(x) = -30x^(4) - 36x^(3) + 3x^(2) + 0.

For the following equation, find $f^{\prime}(x)$ . $\newline$ $f(x)=-6 x^{5}-9 x^{4}+x^{3}+6$ $\newline$ Answer: $f^{\prime}(x)=$

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For the following equation, find f′(x) f^{\prime}(x) f′(x).\newlinef(x)=−6x5−9x4+x3+6 f(x)=-6 x^{5}-9 x^{4}+x^{3}+6 f(x)=−6x5−9x4+x3+6\newlineAnswer: f′(x)= f^{\prime}(x)= f′(x)=

For the following equation, find $f^{\prime}(x)$ . $\newline$ $f(x)=-6 x^{5}-9 x^{4}+x^{3}+6$ $\newline$ Answer: $f^{\prime}(x)=$