The Power Rule (Delehant)

Front

What is the Power Rule in calculus?

Back

The Power Rule states that if f(x) = x^n, then the derivative f'(x) = n*x^(n-1).

Front

How do you find the derivative of f(x) = x^5?

Back

Using the Power Rule: f'(x) = 5*x^(5-1) = 5x^4.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is zero.

Front

Find the derivative of f(x) = 2x^3 + 4x^2 - 5.

Back

f'(x) = 6x^2 + 8x.

Front

What does it mean for the slope of the tangent line to be zero?

Back

It means that the function has a local maximum or minimum at that point.

Front

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

Back

f'(x) = 12x^3 - 2.

Front

What is the derivative of f(x) = x^n when n is a negative integer?

Back

f'(x) = n*x^(n-1), where n is negative.

Front

Find the derivative of f(x) = 5x^2 + 3x + 7.

Back

f'(x) = 10x + 3.

Front

What is the significance of the derivative in relation to a function's graph?

Back

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

Front

Find the derivative of f(x) = x^6 - 4x^3 + 2.

Back

f'(x) = 6x^5 - 12x^2.