Calc AB Unit 2-3 Test Review

Front

What is the product rule for differentiation?

Back

The product rule states that if you have two functions u(x) and v(x), the derivative of their product is given by: \( (uv)' = u'v + uv' \).

Front

Find the derivative of \( f(x) = 4x(3x-1)^2 \).

Back

\( f'(x) = 24x(3x-1) + 4(3x-1)^2 \)

Front

What is the chain rule in calculus?

Back

The chain rule is used to differentiate composite functions. If \( y = f(g(x)) \), then the derivative is given by: \( \frac{dy}{dx} = f'(g(x)) \cdot g'(x) \).

Front

Find \( h'(3) \) if \( h(x) = x^2 - 9 \).

Back

\( h'(3) = 1 \)

Front

Find the derivative of \( y = \cos^5(x) \).

Back

\( \frac{dy}{dx} = -5\cos^4(x)\sin(x) \)

Front

What is the power rule for differentiation?

Back

The power rule states that if \( f(x) = x^n \), then \( f'(x) = nx^{n-1} \).

Front

Find the derivative of \( f(x) = 6x^{30} - 2x^{15} + 4x^3 - 2x + 1 \).

Back

\( f'(x) = 180x^{29} - 30x^{14} + 12x^{2} - 2 \)

Front

What is the derivative of a constant?

Back

The derivative of a constant is zero. If \( c \) is a constant, then \( \frac{d}{dx}(c) = 0 \).

Front

How do you find the derivative of a function at a specific point?

Back

To find the derivative at a specific point, calculate the derivative function and then substitute the x-value into that derivative.

Front

What is the significance of the derivative in calculus?

Back

The derivative represents the rate of change of a function with respect to its variable, indicating how the function behaves as its input changes.