Derivative Power Rule and Def of Derivative

Front

What is the Derivative Power Rule?

Back

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

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point.

Front

Differentiate y = x^3.

Back

y' = 3x^2.

Front

What is the slope of the tangent line to y = x^2 at x = 2?

Back

The slope is 4.

Front

Differentiate y = 5x^4.

Back

y' = 20x^3.

Front

What is the equation of the tangent line to y = x^2 at the point (1, 1)?

Back

y = 2x - 1.

Front

Differentiate y = 7x^5 - 3x^2 + 2.

Back

y' = 35x^4 - 6x.

Front

What is the slope of the tangent line to y = -2x^2 + 3 at x = 1?

Back

The slope is -4.

Front

Differentiate y = 1/x.

Back

y' = -1/x^2.

Front

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

Back

y' = cos(x).