Product and Quotient Rule

Front

What is the Product Rule in calculus?

Back

The Product Rule states that if you have two functions u(x) and v(x), the derivative of their product is given by: (u*v)' = u'v + uv'.

Front

What is the Quotient Rule in calculus?

Back

The Quotient Rule states that if you have two functions u(x) and v(x), the derivative of their quotient is given by: (u/v)' = (u'v - uv')/v^2.

Front

How many derivatives can you take of a function?

Back

Until you can no longer derive it.

Front

Find the derivative of g(x) = (3x - 2)/(x^2 + 2).

Back

g'(x) = (-3x^2 + 4x + 6)/(x^2 + 2)^2.

Front

What does the derivative represent in a graph?

Back

The derivative represents the slope of the tangent line to the curve at a given point.

Front

Find an equation of the line tangent to the curve f(x) = (x - 2)(x + 1) at the point (1, 3).

Back

y = x + 2.

Front

Find the derivative of y = 2x^2(3x - 4).

Back

y' = 18x^2 - 16x.

Front

What is the relationship between the derivative and the slope of a tangent line?

Back

The derivative at a point gives the slope of the tangent line to the curve at that point.

Front

If f(x) = x^3, what is f'(x)?

Back

f'(x) = 3x^2.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.