Derivatives of Polynomial Functions | Calculus

TL;DR

Learn how to find the derivative of a polynomial function by applying the power rule and constant multiple rule.

Transcript

in this lesson we're going to go over derivatives of polynomial functions so let's say if we have the function f of x and it's x cubed minus 5 x squared plus seven x minus four so what is the derivative of that function so all you need to do is find the derivative of each term separately so using the power rule the derivative of x cubed is going to... Read More

Key Insights

• 📏 Applying the power rule and constant multiple rule are the key steps in finding the derivative of a polynomial function.
• 🍉 Differentiating each term of the polynomial function separately is crucial in obtaining the correct derivative.
• 😑 Simplifying the polynomial function before finding its derivative helps to simplify the expression and make the differentiation process easier.

Questions & Answers

Q: How do you find the derivative of a polynomial function?

To find the derivative of a polynomial function, differentiate each term separately using the power rule and constant multiple rule. Apply the power rule by multiplying the exponent by the coefficient and reducing the exponent by 1. Use the constant multiple rule by multiplying the derivative of the term by the constant coefficient.

Q: What is the power rule?

The power rule states that to find the derivative of a term with an exponent, multiply the exponent by the coefficient and reduce the exponent by 1.

Q: How do you apply the constant multiple rule?

The constant multiple rule states that to find the derivative of a term multiplied by a constant, multiply the derivative of the term by the constant coefficient.

Q: How do you simplify a polynomial function before finding its derivative?

To simplify a polynomial function before finding its derivative, divide each term of the polynomial by a monomial divisor. Subtract the exponents of the variables when dividing.

Summary & Key Takeaways

• To find the derivative of a polynomial function, differentiate each term separately using the power rule and constant multiple rule.

• Apply the power rule by multiplying the exponent by the coefficient and reducing the exponent by 1.

• Use the constant multiple rule by multiplying the derivative of the term by the constant coefficient.