Product and Quotient Derivatives

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is zero.

Front

Find the derivative of the function: f(x) = 7.

Back

f'(x) = 0.

Front

What is the power rule for derivatives?

Back

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

Front

Find the derivative of the function: f(x) = 4x^4 - 3x^3 - 9.

Back

f'(x) = 16x^3 - 9x^2.

Front

What is the product rule for derivatives?

Back

If u(x) and v(x) are functions, then (uv)' = u'v + uv'.

Front

Calculate the derivative of f(x) = x^2 sin(x).

Back

f'(x) = x^2 cos(x) + 2x sin(x).

Front

What is the quotient rule for derivatives?

Back

If u(x) and v(x) are functions, then (u/v)' = (u'v - uv')/v^2.

Front

Find the derivative of f(x) = x^3 / (x^2 + 1).

Back

f'(x) = (3x^2(x^2 + 1) - x^3(2x))/(x^2 + 1)^2.

Front

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

Back

The slope of the tangent line is zero at points where the derivative is zero, indicating a local maximum or minimum.

Front

At which points will the slopes of the tangent line be zero for f(x) = x^2 - 4x + 4?

Back

At point B and D only.