Given the function f(x)=(6x^(2)-3)(5-2x^(2)+7x^(-1)), find f^(')(x) in any form. Answer: f^(')(x)=

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Given the function  f(x)=(6x^(2)-3)(5-2x^(2)+7x^(-1)), find  f^(')(x) in any form. Answer:  f^(')(x)=

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Apply Product Rule: To find the derivative of the function f(x)=(6x^(2)-3)(5-2x^(2)+7x^(-1)), we will use the product rule. The product rule states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.Define Functions: Let's denote the first function as u(x) = 6x^2 - 3 and the second function as v(x) = 5 - 2x^2 + 7x^(-1). We will find the derivatives u'(x) and v'(x) separately.Find u'(x): The derivative of u(x) = 6x^2 - 3 with respect to x is u'(x) = d/dx(6x^2) - d/dx(3) = 12x - 0 = 12x.Find v'(x): The derivative of v(x) = 5 - 2x^2 + 7x^(-1) with respect to x is v'(x) = d/dx(5) - d/dx(2x^2) + d/dx(7x^(-1)) = 0 - 4x + (-7)x^(-2) = -4x - 7x^(-2).Apply Product Rule Again: Now we apply the product rule: f'(x) = u'(x)v(x) + u(x)v'(x). Substituting the derivatives we found, we get f'(x) = (12x)(5 - 2x^2 + 7x^(-1)) + (6x^2 - 3)(-4x - 7x^(-2)).Distribute Terms: We will now distribute the terms in the expression for f'(x): f'(x) = 12x(5) - 12x(2x^2) + 12x(7x^(-1)) - (6x^2)(4x) - (6x^2)(7x^(-2)) - 3(-4x) - 3(-7x^(-2)).Simplify Expression: Simplify the expression by performing the multiplications: f'(x) = 60x - 24x^3 + 84x^0 - 24x^3 - 42x^0 - 12x + 21x^(-2).Combine Like Terms: Combine like terms in the expression for f'(x): f'(x) = (60x - 12x) - (24x^3 + 24x^3) + (84 - 42) + 21x^(-2).Final Answer: After combining like terms, we get f'(x) = 48x - 48x^3 + 42 + 21x^(-2).We have found the derivative of the function f(x) in its simplified form. The final answer is f'(x) = 48x - 48x^3 + 42 + 21x^(-2).

Given the function $f(x)=\left(6 x^{2}-3\right)\left(5-2 x^{2}+7 x^{-1}\right)$ , find $f^{\prime}(x)$ in any form. $\newline$ Answer: $f^{\prime}(x)=$

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Given the function f(x)=(6x2−3)(5−2x2+7x−1) f(x)=\left(6 x^{2}-3\right)\left(5-2 x^{2}+7 x^{-1}\right) f(x)=(6x2−3)(5−2x2+7x−1), find f′(x) f^{\prime}(x) f′(x) in any form.\newlineAnswer: f′(x)= f^{\prime}(x)= f′(x)=

Given the function $f(x)=\left(6 x^{2}-3\right)\left(5-2 x^{2}+7 x^{-1}\right)$ , find $f^{\prime}(x)$ in any form. $\newline$ Answer: $f^{\prime}(x)=$