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  2. AP Calculus
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Explain the concept of the Power Rule.

Multiply the coefficient by the exponent and reduce the exponent by one.

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Explain the concept of the Power Rule.

Multiply the coefficient by the exponent and reduce the exponent by one.

Why is rewriting functions important when applying the Power Rule?

It allows us to apply the Power Rule to radicals and fractions by expressing them as powers.

Why does the derivative of a constant equal zero?

Because a constant function has no change; its rate of change is zero.

What is the Power Rule formula?

f(x)=xnRightarrowf′(x)=ncdotx(n−1)f(x) = x^n Rightarrow f'(x) = n cdot x^{(n-1)}f(x)=xnRightarrowf′(x)=ncdotx(n−1)

What is the derivative of a constant?

f(x)=cRightarrowf′(x)=0f(x) = c Rightarrow f'(x) = 0f(x)=cRightarrowf′(x)=0

Define the Power Rule.

A method to find the derivative of power functions of the form f(x)=xnf(x) = x^nf(x)=xn.

What is a power function?

A function in the form f(x)=xnf(x) = x^nf(x)=xn, where n is a constant.

What is a derivative?

The instantaneous rate of change of a function.

What does it mean to rewrite a function?

Changing the form of a function without changing its value, often to make differentiation easier.