How to Find Derivatives Using Power Rule and Examples

TL;DR

To find derivatives, use the power rule which states the derivative of x^n is n*x^(n-1). The derivative of a constant is zero, while the derivative of a constant multiplied by a function is the constant multiplied by the derivative of that function. For polynomials, take the derivative of each term and sum them together.

Transcript

in this lesson we're going to focus on finding the derivative of a function so let's start with a constant the derivative of any constant is equal to zero so for instance the derivative of the constant 5 is 0 and the derivative let's say of negative 7 is also 0 and you might be wondering what exactly is a derivative a derivative is a function that ... Read More

Key Insights

• ✊ The power rule is a useful tool for finding the derivative of monomials.
• 👻 The constant multiple rule allows us to find the derivative of functions multiplied by a constant.
• 🍉 The derivative of a polynomial function can be found by finding the derivative of each term individually and then adding them together.
• 0️⃣ The derivative of a constant is always zero.
• ☺️ The derivative of a function gives the slope of the function at a specific x value.

Questions & Answers

Q: What is the derivative of a constant?

The derivative of a constant is always zero. This is because the slope of a constant function is always zero.

Q: What is the power rule?

The power rule states that the derivative of a variable raised to a constant power is equal to the constant times the variable raised to the power minus one. This rule is helpful for finding the derivative of monomials.

Q: How do you find the derivative using the constant multiple rule?

The constant multiple rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function. This rule allows us to easily find the derivative of functions that are multiplied by a constant.

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

To find the derivative of a polynomial function, you need to find the derivative of each term individually and then add them together. This can be done using the power rule and the constant multiple rule.

Summary & Key Takeaways

• The derivative of a constant is always zero, and the derivative of a monomial can be found using the power rule.

• The power rule states that the derivative of a variable raised to a constant power is equal to the constant times the variable raised to the power minus one.

• The derivative of a function can be found using the constant multiple rule, which states that the derivative of a constant times a function is equal to the constant times the derivative of the function.

• The derivative of a polynomial function can be found by finding the derivative of each term individually and then adding them together.