Derivatives

Front

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

Back

f'(x) = 3x^2 + 2x.

Front

Find the slope of f(x) = -3x^2 - 6x at x = 1.

Back

f'(1) = -12.

Front

What is the derivative of y = 4x^2 + 4x + 1?

Back

y' = 8x + 4.

Front

What does it mean if the derivative of a function is positive?

Back

The function is increasing.

Front

What does it mean if the derivative of a function is negative?

Back

The function is decreasing.

Front

What is the derivative of f(x) = x^2?

Back

f'(x) = 2x.

Front

Write the equation of the tangent line to the graph of y = x^2 at point (1, 1).

Back

y = 2x - 1.

Front

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

Back

f'(x) = cos(x).

Front

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

Back

f'(x) = e^x.

Front

What is the power rule for derivatives?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).