Understanding Derivatives with Radicals

The video tutorial explains how to find the derivative of a function containing radicals by first converting the radicals into rational exponents. It then demonstrates the application of the power rule of differentiation to simplify the function and find its derivative. The tutorial concludes by rewriting the derivative in radical form for clarity.

What is the first step in finding the derivative of a function containing radicals?

• Apply the power rule directly.

• Convert radicals to rational exponents.

• Simplify the function using algebraic identities.

• Rewrite the function in terms of trigonometric identities.

How do you express the square root of x using rational exponents?

• x^(1/3)

• x^2

• x^(1/2)

• x^(2/1)

What is the result of adding the exponents 4 and 1/2?

• 5

• 4.5

• 9/2

• 8/2

What happens to the exponent when you move a term from the denominator to the numerator?

• The exponent doubles.

• The exponent's sign changes.

• The exponent remains unchanged.

• The exponent becomes zero.

What is the derivative of x^(9/2) using the power rule?

• 9/2 * x^(7/2)

• 9 * x^(7/2)

• x^(9/2)

• x^(7/2)

How do you simplify the expression 9x^(7/2) + 28/3x^(-10/3) using positive exponents?

• 9x^(7/2) + 28/(3x^(10/3))

• 9x^(7/2) + 28x^(10/3)

• 9x^(7/2) + 28/3x^(10/3)

• 9x^(7/2) - 28/3x^(10/3)

What is the cube root of x^10 simplified to?

• x^9

• cube root of x^10

• x^10

• x^3 * cube root of x

How can x^7 be expressed to simplify the square root?

• x^5 * x^2

• x^3 * x^4

• x^7

• x^6 * x

What is the simplified form of the square root of x^6?

• x^4

• x^2

• x^6

• x^3

Why might it be necessary to rewrite a derivative function back in radical form?

• To simplify the calculation of limits.

• To comply with specific problem requirements.

• To make it easier to integrate.

• To convert it into a polynomial.