Derivatives Basic Rules

Front

What is the notation for the derivative of a function?

Back

Common notations include f'(x), y', and dy/dx. However, dy is not a correct notation for the derivative.

Front

What is the Power Rule for derivatives?

Back

Front

What is the derivative of a constant?

Back

The derivative of any constant is 0.

Front

What is the derivative of the function f(x) = e^π?

Back

f'(x) = 0, since e^π is a constant.

Front

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

Back

f'(x) = 3x^2.

Front

What is the derivative of f(x) = 5x^4?

Back

f'(x) = 20x^3.

Front

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

Back

f'(x) = 0, since 7 is a constant.

Front

What is the derivative of f(x) = x^0?

Back

f'(x) = 0, since x^0 = 1, which is a constant.

Front

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

Back

f'(x) = nx^{n-1}, following the Power Rule.

Front

What is the derivative of f(x) = x^{-2}?

Back

f'(x) = -2x^{-3}.