**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.

**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)` (x^{3} + 4)

= e^{(x^3 + 4)} (3x^{2})

= 3x^{2} e^{(x^3 + 4)}

**Example problem 3:**

**Find the derivative for the function y = e ^{cosec (7x)} + e^{2x}**

**Solution:**

Step 1: Given function

y = e^{cosec (7x)} + e^{2x}

Step 2: Differentiate the given function y = e^{cosec (7x)} + e^{2x} with respect to ' x ', to get `(dy)/(dx)`

`(dy)/(dx)` = e^{cosec (7x)} (- 7cosec (7x) cot (7x)) + e^{2x} (2)

= - 7e^{cosec (7x)} cosec (7x) cot (7x) + 2e^{2x}

1) Find the derivative for the function y = 2e^{12x}

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

3) Find the derivative for the function y = e^{cos (7x)} + e^{-x}

**Solutions:**

1) 24e^{12x}

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

3) - 7e^{cos (7x)} sin (7x) - e^{-x}