Differentiation and Derivative Functions

The video tutorial explains how to find the derivative of a function using the product rule. It begins with an introduction to the function and the need for differentiation. The product rule is applied to differentiate the function, followed by calculating the derivatives of individual terms. The tutorial then demonstrates how to simplify the derivative expression and factor it to find common factors. The video concludes with presenting the derivative in both simplified and factored forms.

What is the initial function F(x) that we are trying to differentiate?

• F(x) = 7x^4 * ln(x) + 45x^5

• F(x) = 7x^4 * ln(x) + 45x^6

• F(x) = 7x^3 * ln(x) + 45x^4

• F(x) = 7x^5 * ln(x) + 45x^4

Which rule is necessary to differentiate the product of two functions?

• Product Rule

• Quotient Rule

• Power Rule

• Chain Rule

What is the derivative of ln(x)?

• ln(x)

• x

• 1/x

• x^2

How do you find the derivative of 7x^4?

• Multiply by 2 and subtract 1 from the exponent

• Multiply by 3 and subtract 1 from the exponent

• Multiply by 5 and subtract 1 from the exponent

• Multiply by 4 and subtract 1 from the exponent

What is the derivative of 45x^5?

• 225x^4

• 45x^4

• 5x^4

• 4x^5

What is the simplified form of the term 7x^4 / x?

• 7x^4

• 7x^2

• 7x^5

• 7x^3

What is the simplified form of the term 5/5?

• 1

• 5

• 0

• 10

What is the derivative function in its standard form?

• 7x^3 + 28x^3 ln(x) + 5x^4

• 7x^3 + 28x^3 ln(x) + 4x^4

• 7x^4 + 28x^3 ln(x) + 4x^5

• 7x^3 + 28x^4 ln(x) + 4x^5

What is the greatest common factor in the derivative function?

• x^3

• x^4

• x^2

• x^5

What is the factored form of the derivative function?

• x^4(7 + 28 ln(x) + 4x)

• x^3(7 + 28 ln(x) + 5x)

• x^3(7 + 28 ln(x) + 4x)

• x^2(7 + 28 ln(x) + 4x)