So we have polynomials in the numerator and denominator of this function so that tells us we need to use the quotient rule:. When differentiating the numerator we need to first take the power rule because the polynomial is raised to a power: , so we bring the 4 down and subtract one. But then the function itself needs to differentiated by means of the chain rule: . The derivative of is just . As for the denominator we have two polynomials multiplied together, so we need to use the product rule which holds one half of the product untouched while differentiating the other half: . For either polynomial we just proceed with the same rules as we did when differentiating the numerator, we first apply the power rule then apply the chain rule to differentiate the functions inside the parentheses.
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