Derivative Rules of Constant, Sum, Difference - AP Calculus BC

21x^2. Apply constant multiple rule: $7 \cdot 3x^2 = 21x^2$.

3x^2 + 2x + 1. Apply power rule to each term.

2x - 2. Apply difference rule: $2x - 2$.

21x^2. Apply constant multiple rule: $7 \cdot 3x^2 = 21x^2$.

6x + 2. Apply power rule to each term.

$-3x^2$. Constant term has zero derivative.

20x^3. Apply constant multiple rule: $5 \cdot 4x^3 = 20x^3$.

1. Any constant has zero derivative.

9x^2 - 4. Differentiate each term using power rule.

$0$. Any constant has zero derivative.

12x^2. Derivative of $4x^3$ is $12x^2$, constant disappears.

$4x + 5$. Differentiate each term separately.

9x^2 + 4. Apply sum rule: $9x^2 + 4$.

10x. Apply constant multiple rule: $5 \cdot 2x = 10x$.

10x + 4. Apply power rule to each term.

1. Constants have zero rate of change.

2x - 4. Differentiate each term, constant disappears.

1. Any constant has derivative zero.

12x^2. Apply constant multiple rule: $4 \cdot 3x^2 = 12x^2$.

4x - 3. Differentiate each term, constant disappears.

12x. Derivative of $6x^2$ is $12x$, constant disappears.

1. Any constant has zero derivative.

4x. Apply constant multiple rule: $2 \cdot 2x = 4x$.

1. Derivative of $5x$ is $5$, constant disappears.

1. Zero function has zero derivative.

8x - 7. Apply power rule to each term.

$\frac{d}{dx}[f(x) + g(x)] = f'(x) + g'(x)$. Derivative of sum equals sum of derivatives.

1. Derivative of $x$ is $1$, multiply by $9$.

2 + 6x. Apply sum rule to each term.