All Flashcards

What is a derivative?

The instantaneous rate of change of a function.

What is a constant?

A fixed value that does not change.

Define the Sum Rule.

The derivative of a sum of functions is the sum of their derivatives.

Define the Difference Rule.

The derivative of a difference of functions is the difference of their derivatives.

Define the Constant Multiple Rule.

The derivative of a constant times a function is the constant times the derivative of the function.

Constant Rule Formula

If $f(x) = c$ , then $f'(x) = 0$ .

Sum Rule Formula

If $f(x) = g(x) + h(x)$ , then $f'(x) = g'(x) + h'(x)$ .

Difference Rule Formula

If $f(x) = g(x) - h(x)$ , then $f'(x) = g'(x) - h'(x)$ .

Constant Multiple Rule Formula

If $f(x) = c cdot g(x)$ , then $f'(x) = c cdot g'(x)$ .

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

Apply the sum/difference rule and constant multiple rule: $f'(x) = 6x + 5$ .

Find the derivative of $f(x) = 7$ .

Apply the constant rule: $f'(x) = 0$ .

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

Apply the sum/difference rule and constant multiple rule: $f'(x) = 12x^2 - 2$ .

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

Apply the sum rule, constant rule, and constant multiple rule: $f'(x) = 20x^3$ .

Find the derivative of $f(x) = 2x^2 - 6x$ .

Apply the difference rule and constant multiple rule: $f'(x) = 4x - 6$ .