AB Derivatives Review

Front

What is the second derivative of f(x) = x² + e^x - cos(x)?

Back

f''(x) = 2 + e^x + cos(x)

Front

If a function has a derivative that is negative, what does that tell you?

Back

The function is decreasing.

Front

Find the derivative of y = 5x²e^(3x).

Back

y' = 5xe^(3x)(3x + 2)

Front

Differentiate y = 12x^(-2).

Back

y' = -24x^(-3)

Front

Find the derivative of f(x) = x^4 + 4x³ - 2x².

Back

f'(x) = 4x³ + 12x² - 4x

Front

What does the first derivative of a function represent?

Back

The first derivative represents the rate of change or the slope of the function.

Front

What is the product rule for differentiation?

Back

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

Front

What is the chain rule for differentiation?

Back

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

Front

What does a positive second derivative indicate about a function?

Back

A positive second derivative indicates that the function is concave up.

Front

What is the derivative of e^(kx) where k is a constant?

Back

The derivative is k * e^(kx).