Derivatives - Product and Quotient Rule

Front

What is the Product Rule for derivatives?

Back

If u(x) and v(x) are functions, then the derivative of their product is given by: (u*v)' = u'v + uv'.

Front

What is the Quotient Rule for derivatives?

Back

If u(x) and v(x) are functions, then the derivative of their quotient is given by: (u/v)' = (u'v - uv')/v^2.

Front

What does it mean for the slope of a tangent line to equal zero?

Back

It indicates that the function has a local maximum or minimum at that point.

Front

How do you find the first derivative of a function?

Back

Use the rules of differentiation (Power Rule, Product Rule, Quotient Rule) to compute the derivative.

Front

What is the Power Rule for derivatives?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What is the second derivative of a function?

Back

The second derivative is the derivative of the first derivative, indicating the rate of change of the rate of change.

Front

How do you find f'(0) for f(x) = (x - 1)(x + 2)?

Back

Use the Product Rule: f'(x) = (x - 1)'(x + 2) + (x - 1)(x + 2)'. Evaluate at x = 0 to get f'(0) = 1.

Front

What is the derivative of f(x) = 2x^3 - 4x + 6?

Back

f'(x) = 6x^2 - 4.

Front

What is the significance of the second derivative being zero?

Back

It may indicate a point of inflection where the concavity of the function changes.

Front

How do you apply the Quotient Rule to find the derivative of f(x) = g(x)/h(x)?

Back

Use (g/h)' = (g'h - gh')/h^2.