AP Calc AB Semester 1 Final Review

Front

What is the derivative of f(x) = x^4 cos(x)?

Back

f'(x) = x^4 cos(x) + 4x^3 sin(x)

Front

Find the derivative of f(x) = (3x + 5)^4.

Back

f'(x) = 12(3x + 5)^3

Front

What does the Mean Value Theorem state?

Back

If f is continuous on [a, b] and differentiable on (a, b), then there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

Front

Identify the incorrect notation for 'derivative'.

Back

dy

Front

Find the derivative of f(x) = x^2 / e^x.

Back

f'(x) = (2xe^x - x^2 e^x) / (e^x)^2

Front

What is the product rule for derivatives?

Back

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

Front

What is the quotient rule for derivatives?

Back

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

Front

What is the chain rule for derivatives?

Back

If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

What is the derivative of sin(x)?

Back

The derivative of sin(x) is cos(x).

Front

What is the derivative of cos(x)?

Back

The derivative of cos(x) is -sin(x).