**Introduction to derivative:**

Derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some
other quantity. The derivative of the position of a vehicle with respect to time is the instantaneous velocity at which the vehicle is traveling.

**Derivative of power x example problem 1:**

Find the derivative value of the 2 to the power x.

**Solution:**

Given value is 2^{x}

Using the differentiation formula,

`(d / dx)` (x^{n}) = nx^{(n -1)}

Form the given value is 2^{x}

We know the formula,

nx = log (n^{x})

Therfore, differntiate the given value, we get

`(d / dx)` (2^{x}) =
log_{2}(2^{x})

**Answer:**

The final answer is log_{2}(2^{x})

**Derivative of power x example problem 2:**

Find the derivative value of the 5 to the power x.

**Solution:**

Given value is 5^{x}

Using the differentiation formula,

`(d / dx)` (x^{n}) = nx^{(n -1)}

Form the given value is 5^{x}

We know the formula,

nx = log (n^{x})

Therfore, differntiate the given value, we get

`(d / dx)` (5^{x}) =
log_{5}(5^{x})

**Answer:**

The final answer is log_{5}(5^{x})

**Derivative of power x example problem 3:**

Find the derivative value of the 7 to the power x.

**Solution:**

Given value is 7^{x}

Using the differentiation formula,

`(d / dx)` (x^{n}) = nx^{(n -1)}

Form the given value is 7^{x}

We know the formula,

nx = log (n^{x})

Therfore, differntiate the given value, we get

`(d / dx)` (7^{x}) =
log_{7}(7^{x})

**Answer:**

The final answer is log_{7}(7^{x})

**Derivative of power x example problem 4:**

Find the derivative value of the 11 to the power x.

**Solution:**

Given value is 11^{x}

Using the differentiation formula,

`(d / dx)` (x^{n}) = nx^{(n -1)}

Form the given value is 11^{x}

We know the formula,

nx = log (n^{x})

Therfore, differntiate the given value, we get

`(d / dx)` (11^{x}) =
log_{11}(11^{x})

**Answer:**

The final answer is log_{11}(11^{x})

Practice problems for derivative of 2 to the power of x

**Derivative of power x practice problem 1:**

Find the derivative value of the 31 to the power x.

**Answer:**

The final answer is log_{31}(31^{x})

**Derivative of power x practice problem 2:**

Find the derivative value of the 17 to the power x.

**Answer:**

The final answer is log_{17}(17^{x})