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.

 

Example problems for derivative of 2 to the power of x

 

Derivative of power x example problem 1:

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

Solution:

  Given value is 2x    

Using the differentiation formula,

            `(d / dx)` (xn) = nx(n -1)

Form the given value is 2x

We know the formula,

                                       nx = log (nx)

Therfore, differntiate the given value, we get

                       `(d / dx)` (2x) = log2(2x)

Answer:

    The final answer is log2(2x)

Derivative of power x example problem 2:

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

Solution:

  Given value is 5x    

Using the differentiation formula,

            `(d / dx)` (xn) = nx(n -1)

Form the given value is 5x

We know the formula,

                                       nx = log (nx)

Therfore, differntiate the given value, we get

                       `(d / dx)` (5x) = log5(5x)

Answer:

    The final answer is log5(5x)

Derivative of power x example problem 3:

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

Solution:

  Given value is 7x    

Using the differentiation formula,

            `(d / dx)` (xn) = nx(n -1)

Form the given value is 7x

We know the formula,

                                       nx = log (nx)

Therfore, differntiate the given value, we get

                       `(d / dx)` (7x) = log7(7x)

Answer:

    The final answer is log7(7x)

Derivative of power x example problem 4:

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

Solution:

  Given value is 11x    

Using the differentiation formula,

            `(d / dx)` (xn) = nx(n -1)

Form the given value is 11x

We know the formula,

                                       nx = log (nx)

Therfore, differntiate the given value, we get

                       `(d / dx)` (11x) = log11(11x)

Answer:

The final answer is log11(11x)

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 log31(31x)

Derivative of power x practice problem 2:

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

Answer:

    The final answer is log17(17x)