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Latte'
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I'm trying to take the derivative of [x/x^2+1]^3. Where do I start?
Start by clarifying your expression.Latte' said:I'm trying to take the derivative of [x/x^2+1]^3. Where do I start?
In the future, post questions like this in the Homework & Coursework section (under Calculus), not here in the technical sections. When you post a question in the Homework section, a template appears into which you enter the problem description, any formulas or equations, and what you have tried.Latte' said:I'm trying to take the derivative of [x/x^2+1]^3. Where do I start?
The derivative of a fraction is calculated by using the quotient rule, which states that the derivative of a fraction is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared.
The power rule for derivatives states that the derivative of a function raised to a power is equal to the power multiplied by the function raised to the power minus one, all multiplied by the derivative of the function.
Yes, the chain rule can be applied to fractions and powers. When taking the derivative of a function within a fraction or power, the chain rule is used to find the derivative of the inner function, and then this derivative is multiplied by the derivative of the outer function.
To simplify a fraction with a variable in the denominator, you can use the power rule for derivatives to rewrite the fraction as a single term. Then, you can solve for the derivative of the numerator and denominator separately, and simplify the resulting fraction.
The main difference between a derivative of a fraction and a derivative of a power is the rule used to calculate them. The derivative of a fraction uses the quotient rule, while the derivative of a power uses the power rule. Additionally, the derivative of a fraction may result in a fraction, while the derivative of a power may result in a polynomial expression.