For the following equation, evaluate f^(')(1). f(x)=-3x^(5)+4x^(3)-2x Answer:

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For the following equation, evaluate  f^(')(1).  f(x)=-3x^(5)+4x^(3)-2x Answer:

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Apply Power Rule: To find the derivative of the function f(x) = -3x^(5) + 4x^(3) - 2x, 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 -3x^(5): First, we find the derivative of the term -3x^(5). Using the power rule, we get: (d)/(dx)(-3x^(5)) = -3 * 5 * x^(5-1) = -15x^(4).Derivative of 4x^(3): Next, we find the derivative of the term 4x^(3). Again, using the power rule, we get: (d)/(dx)(4x^(3)) = 4 * 3 * x^(3-1) = 12x^(2).Derivative of -2x: Finally, we find the derivative of the term -2x. The power rule for the first power is simply the coefficient, so: (d)/(dx)(-2x) = -2.Combine Derivatives: Now, we combine the derivatives of each term to get the derivative of the entire function f(x): f^(')(x) = -15x^(4) + 12x^(2) - 2.Evaluate f^(')(1): To evaluate f^(')(1), we substitute x = 1 into the derivative: f^(')(1) = -15(1)^(4) + 12(1)^(2) - 2 = -15 + 12 - 2.Perform Arithmetic: Performing the arithmetic, we get: f^(')(1) = -15 + 12 - 2 = -5.

For the following equation, evaluate $f^{\prime}(1)$ . $\newline$ $f(x)=-3 x^{5}+4 x^{3}-2 x$ $\newline$ Answer:

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For the following equation, evaluate f′(1) f^{\prime}(1) f′(1).\newlinef(x)=−3x5+4x3−2x f(x)=-3 x^{5}+4 x^{3}-2 x f(x)=−3x5+4x3−2x\newlineAnswer:

For the following equation, evaluate $f^{\prime}(1)$ . $\newline$ $f(x)=-3 x^{5}+4 x^{3}-2 x$ $\newline$ Answer: