Given the function f(x)=(x)/(1-2x^(4)), find f^(')(x) in simplified form. Answer: f^(')(x)=

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Given the function  f(x)=(x)/(1-2x^(4)), find  f^(')(x) in simplified form. Answer:  f^(')(x)=

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Quotient Rule Explanation: To find the derivative of the function f(x) = (x)/(1-2x^(4)), we will use the quotient rule. The quotient rule states that if we have a function that is the quotient of two functions, u(x)/v(x), then its derivative f'(x) is given by (v(x)u'(x) - u(x)v'(x))/(v(x))^2. Here, u(x) = x and v(x) = 1 - 2x^(4).Find u'(x): First, we need to find the derivative of u(x), which is u'(x). Since u(x) = x, the derivative u'(x) is 1 because the derivative of x with respect to x is 1.Find v'(x): Next, we need to find the derivative of v(x), which is v'(x). Since v(x) = 1 - 2x^(4), we apply the power rule to find the derivative of -2x^(4). The power rule states that the derivative of x^n with respect to x is n*x^(n-1). Therefore, v'(x) = 0 - 2*4*x^(4-1) = -8x^(3).Apply Quotient Rule: Now we apply the quotient rule. We have u'(x) = 1 and v'(x) = -8x^(3), so we plug these into the quotient rule formula:  f'(x) = ( (1 - 2x^(4))(1) - (x)(-8x^(3)) ) / (1 - 2x^(4))^2Simplify Derivative: Simplify the numerator of the derivative:  f'(x) = (1 - 2x^(4) - (-8x^(4))) / (1 - 2x^(4))^2 f'(x) = (1 - 2x^(4) + 8x^(4)) / (1 - 2x^(4))^2 f'(x) = (1 + 6x^(4)) / (1 - 2x^(4))^2

Given the function $f(x)=\frac{x}{1-2 x^{4}}$ , find $f^{\prime}(x)$ in simplified form. $\newline$ Answer: $f^{\prime}(x)=$

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Given the function $f(x)=\frac{x}{1-2 x^{4}}$ , find $f^{\prime}(x)$ in simplified form. $\newline$ Answer: $f^{\prime}(x)=$