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  1. AP Calculus
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Find the derivative of f(x)=3x2+5x−2f(x) = 3x^2 + 5x - 2f(x)=3x2+5x−2.

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

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Find the derivative of f(x)=3x2+5x−2f(x) = 3x^2 + 5x - 2f(x)=3x2+5x−2.

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

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

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

Find the derivative of f(x)=4x3−2x+1f(x) = 4x^3 - 2x + 1f(x)=4x3−2x+1.

Apply the sum/difference rule and constant multiple rule: f′(x)=12x2−2f'(x) = 12x^2 - 2f′(x)=12x2−2.

Find the derivative of f(x)=5x4+3f(x) = 5x^4 + 3f(x)=5x4+3.

Apply the sum rule, constant rule, and constant multiple rule: f′(x)=20x3f'(x) = 20x^3f′(x)=20x3.

Find the derivative of f(x)=2x2−6xf(x) = 2x^2 - 6xf(x)=2x2−6x.

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

Explain the Constant Rule.

The derivative of a constant is always zero because a constant's value does not change.

Explain the Sum Rule.

When differentiating a sum of functions, you can differentiate each function separately and then add the results.

Explain the Difference Rule.

When differentiating a difference of functions, you can differentiate each function separately and then subtract the results.

Explain the Constant Multiple Rule.

A constant multiplying a function remains as a multiplier when you take the derivative of the function.

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.