Introduction to derivative of the exponential function tutor:

The derivative (rate of change) of the exponential function is the exponential function itself. More generally, a function with a rate of change proportional to the function itself is expressible in terms of the exponential function.

 

It is very easy for the students to learn derivative of exponential function from the tutor. The tutor explains every single topic with example problems, which can be easily understandable by the students. The tutors give the home work problems, assignments and conduct test to the students for learning derivative of exponential function. A few example problems are given below to show how tutors help you for learning derivatives of exponential function.

                                                                                                                          

Learning derivative of exponential function with example problems from the tutor:

 

Example problem 1:

Find the derivative for the function y = 2e-11x 

Solution:

Step 1: Given function

                                 y = 2e-11x

Step 2: Differentiate the given function y = 2e-11x with respect to ' x ', to get `(dy)/(dx)`

                                `(dy)/(dx)` = 2e-11x `d/(dx)` (-11x)

                                       = 2e-11x (-11)

                                       = - 22 e-11x

Example problem 2:

Find the derivative for the function y = e(x^3 + 4)  

Solution:

Step 1: Given function

                                 y = e(x^3 + 4)

Step 2: Differentiate the given function y = e(x^3 + 4) with respect to ' x ', to get `(dy)/(dx)`

                                `(dy)/(dx)` = e(x^3 + 4) `d/(dx)` (x3 + 4)

                                       = e(x^3 + 4) (3x2)

                                                    = 3x2 e(x^3 + 4)

Example problem 3:

Find the derivative for the function y = ecosec (7x) + e2x 

Solution:

 Step 1: Given function

                                 y = ecosec (7x) + e2x

Step 2: Differentiate the given function y = ecosec (7x) + e2x with respect to ' x ', to get `(dy)/(dx)`

`(dy)/(dx)` = ecosec (7x) (- 7cosec (7x) cot (7x)) + e2x (2)

= - 7ecosec (7x) cosec (7x) cot (7x) + 2e2x

 

Learning derivative of exponential function with practice problems from the tutor:

 

1) Find the derivative for the function y = 2e12x

2) Find the derivative for the function y = e(x^2 + 7x)

3) Find the derivative for the function y = ecos (7x) + e-x

Solutions:

1) 24e12x

2) (2x + 7)xe(x^2 + 7x)

3) - 7ecos (7x) sin (7x) - e-x