derivatives - power rule

Front

What is the power rule for derivatives?

Back

The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).

Front

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

Back

f'(x) = 4x^3.

Front

What is the derivative of a constant function, f(x) = c?

Back

The derivative is 0.

Front

Differentiate y = 12x^-2.

Back

y' = -24x^-3.

Front

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

Back

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

Front

What does the derivative represent in terms of a function's graph?

Back

The derivative represents the slope of the tangent line to the graph of the function at a given point.

Front

At which points is the slope of the tangent line positive for f(x) = x^2?

Back

At points where x > 0.

Front

If f(x) = x^5, what is f'(x)?

Back

f'(x) = 5x^4.

Front

What is the derivative of f(x) = 7x^3?

Back

f'(x) = 21x^2.

Front

Differentiate y = 5x^4 - 3x + 2.

Back

y' = 20x^3 - 3.