AP Calculus Derivative Rules (no a^x or log base b yet)

Front

What is the product rule for derivatives?

Back

If \( f(x) \) and \( g(x) \) are functions, then the derivative of their product is given by: \( \frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x) \).

Front

What is the quotient rule for derivatives?

Back

If \( f(x) \) and \( g(x) \) are functions, then the derivative of their quotient is given by: \( \frac{d}{dx}\left[\frac{f(x)}{g(x)}\right] = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2} \).

Front

What is the derivative of \( f(x) = \frac{1}{x^2} \)?

Back

The derivative is \( f'(x) = -\frac{2}{x^3} \).

Front

What is the chain rule for derivatives?

Back

If \( f(g(x)) \) is a composite function, then the derivative is given by: \( \frac{d}{dx}[f(g(x))] = f'(g(x))g'(x) \).

Front

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

Back

The derivative is \( \frac{d}{dx}[\sqrt{x}] = \frac{1}{2\sqrt{x}} \).

Front

What is the power rule for derivatives?

Back

If \( f(x) = x^n \), then the derivative is \( f'(x) = nx^{n-1} \).

Front

What is the derivative of a constant?

Back

The derivative of a constant \( c \) is \( 0 \).

Front

What is the derivative of \( f(x) = x^3 \)?

Back

The derivative is \( f'(x) = 3x^2 \).

Front

What is the derivative of \( f(x) = 5x^4 \)?

Back

The derivative is \( f'(x) = 20x^3 \).

Front

What is the derivative of \( f(x) = 2x^2 + 3x + 1 \)?

Back

The derivative is \( f'(x) = 4x + 3 \).