Derivatives Practice

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

Find the derivative of the function f(x) = 5x^4.

Back

f'(x) = 20x^3.

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 the function f(x) = 2x^3 + 3x^2 - 5.

Back

f'(x) = 6x^2 + 6x.

Front

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

Back

f'(x) = cos(x).

Front

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

Back

f'(x) = -sin(x).

Front

Find the slope of the tangent line to the curve y = 4 - 3x^2 at the point (-1, 1).

Back

The slope is 6.

Front

Find the derivative of the function f(x) = x^3 + x^2 + 3.

Back

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

Front

What is the derivative of f(x) = -4x?

Back

f'(x) = -4.

Front

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

Back

f'(x) = nx^(n-1).