AP Passport Flashcard on Rules for Derivatives & Antiderivatives

Front

What is the derivative of the function y = 8^x?

Back

The derivative is \( \frac{dy}{dx} = \left(\ln 8\right)8^x \)

Front

What is the derivative of \( \cos(x) \)?

Back

The derivative is \( \frac{d}{dx}\left(\cos(x)\right) = -\sin(x) \)

Front

Find the derivative of the function f(x) = \( \frac{x^2}{e^x} \).

Back

The derivative is \( f'(x) = \frac{2xe^x - x^2e^x}{(e^x)^2} \)

Front

What is the derivative of \( \sin(x) \)?

Back

The derivative is \( \frac{d}{dx}\left(\sin(x)\right) = \cos(x) \)

Front

What is the product rule for derivatives?

Back

If \( f(x) \) and \( g(x) \) are functions, then \( \frac{d}{dx}\left[f(x)g(x)\right] = f'(x)g(x) + g'(x)f(x) \)

Front

What is the derivative of \( e^x \)?

Back

The derivative is \( \frac{d}{dx}\left(e^x\right) = e^x \)

Front

What is the chain rule for derivatives?

Back

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

Front

What is the derivative of \( an(x) \)?

Back

The derivative is \( \frac{d}{dx}\left(\tan(x)\right) = \sec^2(x) \)

Front

What is the derivative of \( x^n \)?

Back

The derivative is \( \frac{d}{dx}\left(x^n\right) = nx^{n-1} \)

Front

What is the derivative of \( rac{1}{x} \)?

Back

The derivative is \( \frac{d}{dx}\left(\frac{1}{x}\right) = -\frac{1}{x^2} \)