Quotient Rule For Derivatives

TL;DR

The quotient rule is a formula used to find the derivative of a function in the form of a fraction, and it involves differentiating the numerator and denominator separately.

Transcript

let's say if we want to find the derivative of this function seven x plus four divided by x squared plus five how can we do so how can we find the derivative of a function in a fraction so we need to use something called the quotient rule and here's the formula that you need to be familiar with the derivative of f divided by g is equal to g times f... Read More

Key Insights

• 💁 The quotient rule is used to find the derivative of functions in the form of a fraction.
• 😀 The formula for the quotient rule is (g * f') - (f * g') / g^2, where f is the numerator and g is the denominator.
• 🔌 Differentiate the numerator and denominator separately, and then plug the derivatives into the quotient rule formula.

Questions & Answers

Q: What is the formula for the quotient rule?

The formula for the quotient rule is (g * f') - (f * g') / g^2, where f is the numerator and g is the denominator.

Q: How do you apply the quotient rule to find the derivative of a function in a fraction?

To apply the quotient rule, differentiate the numerator and denominator separately, then plug the derivatives into the formula (g * f') - (f * g') / g^2.

Q: Can you leave the answer in the form of (g * f') - (f * g') / g^2?

Some teachers may allow leaving the answer in that form, but others may require further simplification by combining like terms.

Q: What should be done if further simplification is required?

To simplify the answer, distribute any multiplication, combine like terms, and simplify the expression as much as possible.

Summary & Key Takeaways

• The quotient rule is used to find the derivative of functions in the form of a fraction.

• The formula for the quotient rule states that the derivative of f divided by g is equal to (g * f') - (f * g') / g^2.

• To apply the quotient rule, differentiate both the numerator and denominator separately and then plug them into the formula.