Understanding Derivatives of Fractions

This video tutorial covers the basics of finding derivatives, starting with the power rule for variables raised to a constant. It then explores how to find derivatives of fractions, both when x is in the numerator and the denominator, including handling negative exponents. The tutorial also addresses derivatives involving square roots and concludes with the application of the quotient rule for more complex fractions.

What is the derivative of x^3 using the power rule?

• x^2

• 3x^3

• 3x^2

• 2x^2

If you have a fraction x/9, what is the derivative?

• 1/9

• 9

• x/9

• 0

How do you find the derivative of 8/x using the power rule?

• 8/x^2

• -8/x^2

• -8x^2

• 8x

What is the derivative of 7/x^2?

• -7/x^3

• 7/x^3

• 14/x^3

• -14/x^3

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

• x^2

• x^3

• x^0.5

• x^1

What is the derivative of the square root of x over 5?

• 1/10x^0.5

• 1/5x^0.5

• 1/5√x

• 1/10√x

What is the derivative of 7 divided by the square root of x?

• -7/2x^1.5

• 7/2x^1.5

• -7/2x√x

• 7/2x√x

Which rule is used to find the derivative of a fraction like (5 + 3x)/(x^2 + 7)?

• Product Rule

• Chain Rule

• Power Rule

• Quotient Rule

What is the derivative of a constant?

• The constant itself

• 1

• Undefined

• 0

In the quotient rule, what does 'g' represent in the formula (g*f' - f*g')/g^2?

• Numerator function

• Denominator function

• Derivative of denominator

• Derivative of numerator