Calculating Derivatives and Exponents

This video tutorial focuses on finding higher order derivatives, including second, third, and fourth derivatives. It begins with a polynomial function, applying the power rule to find the second derivative. The tutorial then explores the product rule for a function involving trigonometric terms, followed by finding the third derivative of a radical function. Finally, it demonstrates calculating the fourth derivative from a given second derivative, emphasizing the use of negative exponents and simplification techniques.

What is the first step in finding the second derivative of a polynomial function?

• Use the chain rule

• Find the first derivative

• Simplify the expression

• Apply the product rule

When using the product rule, what is the derivative of the product of two functions f and g?

• f * g' + f' * g'

• f' * g' - f * g

• f' * g + f * g'

• f' * g' + f * g

In the context of derivatives, what does the term 'f prime' refer to?

• The original function

• The integral of the function

• The second derivative

• The first derivative

How do you express the square root of x in terms of exponents?

• x^(3/2)

• x^(-1/2)

• x^(1/2)

• x^2

What is the result of applying the power rule to x^(1/2)?

• x^(-1/2)

• 2 * x^(1/2)

• x^(1/2)

• 1/2 * x^(-1/2)

What is the third derivative of x^(1/2) after simplification?

• 3/8 * x^(3/2)

• 3/8 * x^(-5/2)

• 3/8 * x^(-3/2)

• 3/8 * x^(5/2)

How do you rewrite 5/x^2 in terms of exponents?

• 5 * x^(-1/2)

• 5 * x^(1/2)

• 5 * x^(-2)

• 5 * x^2

What is the fourth derivative of 5x^(-2) after simplification?

• 30/x^4

• 30x^4

• 30/x^2

• 30x^(-4)

What is the result of differentiating x^(-3) using the power rule?

• -3x^(-4)

• 3x^(-4)

• 3x^(-2)

• -3x^(-2)

What is the general approach to finding higher order derivatives?

• Use the chain rule repeatedly

• Differentiate the function multiple times

• Integrate the function multiple times

• Simplify the function and differentiate once