AP Calculus AB Final Exam Fall 2024

Front

What is the product rule for differentiation?

Back

If \( f(x) = g(x)h(x) \), then \( f'(x) = g'(x)h(x) + g(x)h'(x) \).

Front

Differentiate the function \( y = (3x^4 - 7)(5x^2 + 1) \).

Back

\( y' = (3x^4 - 7)(10x) + (12x^3)(5x^2 + 1) \)

Front

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

Back

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

Front

Differentiate \( f(x) = xe^x \).

Back

\( f'(x) = e^x + xe^x \)

Front

What does it mean if \( f'(x) = 0 \)?

Back

The tangent line to the curve at that point is horizontal.

Front

Differentiate \( y = 12x^{-2} \).

Back

\( \frac{dy}{dx} = -\frac{24}{x^3} \)

Front

What is the chain rule for differentiation?

Back

If \( y = f(g(x)) \), then \( \frac{dy}{dx} = f'(g(x))g'(x) \).

Front

What is the power rule for differentiation?

Back

If \( y = x^n \), then \( \frac{dy}{dx} = nx^{n-1} \).

Front

Differentiate \( y = 5x^3 + 2x^2 - 4x + 7 \).

Back

\( \frac{dy}{dx} = 15x^2 + 4x - 4 \)

Front

What is the quotient rule for differentiation?

Back

If \( f(x) = \frac{g(x)}{h(x)} \), then \( f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2} \).