# What is the example of power rule?

## What is the example of power rule?

The power rule in calculus is a fairly simple rule that helps you find the derivative of a variable raised to a power, such as: x^5, 2x^8, 3x^(-3) or 5x^(1/2). All you do is take the exponent, multiply it by the coefficient (the number in front of the x), and decrease the exponent by 1.

## What is power function rule?

The power rule is used to find the slope of polynomial functions and any other function that contains an exponent with a real number. In other words, it helps to take the derivative of a variable raised to a power (exponent).

**When can’t you use the power rule?**

The power rule only works for functions raised to a power, like x^3, x^4, (x+2)^5, or sqrt(x), etc. The power isn’t a variable, it’s a constant. When the power is a variable, like e^x, 2^x, we call that an exponential function, and you can’t use the power rule to differentiate it.

**How do you calculate power rule?**

We can call this “x raised to the power of n,” “x to the power of n,” or simply “x to the n.” Here, x is the base and n is the exponent or the power….Basic rules for exponentiation.

Rule or special case | Formula | Example |
---|---|---|

Power of power | (xa)b=xab | (23)2=26=64 |

Power of a product | (xy)a=xaya | 36=62=(2⋅3)2=22⋅32 |

Power of one | x1=x | 21=2 |

Power of zero | x0=1 | 20=1 |

### How do you find the power rule?

To use the power rule, multiply the variable’s exponent n, by its coefficient a, then subtract 1 from the exponent. If there’s no coefficient (the coefficient is 1), then the exponent will become the new coefficient.

### What is the power rule in integration?

The power rule for integration provides us with a formula that allows us to integrate any function that can be written as a power of x. By the end of this section we’ll know how to evaluate integrals like: ∫4x3dx. ∫3x2dx. ∫(2x+3√x)dx.

**What is the power to power rule in math?**

The power of a power rule states that if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same.

**How do you solve a power rule in integration?**

If you can write it with an exponents, you probably can apply the power rule. To apply the rule, simply take the exponent and add 1. Then, divide by that same value. Finally, don’t forget to add the constant C.

#### What is the simple power formula?

Basic rules for exponentiation

Rule or special case | Formula | Example |
---|---|---|

Power of one | x1=x | 21=2 |

Power of zero | x0=1 | 20=1 |

Power of negative one | x−1=1x | 2−1=12 |

Change sign of exponents | x−a=1xa | 2−3=123=18 |