Derivatives (Power Rule)

Front

What is the Power Rule for derivatives?

Back

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

Front

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

Back

f'(x) = 15x^2.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

How do you find the slope of the tangent line to a curve at a given point?

Back

To find the slope of the tangent line at a point, calculate the derivative of the function and evaluate it at that point.

Front

Find the derivative of f(x) = 2x^4 - 3x + 7.

Back

f'(x) = 8x^3 - 3.

Front

What does the derivative represent in a real-world context?

Back

The derivative represents the rate of change of a quantity with respect to another quantity.

Front

If f(x) = x^2 + 2x, what is f'(1)?

Back

f'(1) = 4.

Front

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

Back

f'(x) = -4.

Front

Explain the concept of a tangent line.

Back

A tangent line is a straight line that touches a curve at a single point and has the same slope as the curve at that point.

Front

Find the derivative of f(x) = 12 - 8x.

Back

f'(x) = -8.