*Notes to a video lecture on http://www.unizor.com*

__Derivatives - Exercise 3__

**Exercise 3.1**Using the rules of taking a derivative, find the derivative of

**f(x) = sin²(x) + cos²(x)**Why the answer is, what it is?

**Exercise 3.2**Using the rules of taking a derivative, find the derivative of

**f(x) = ln(e**^{x})Why the answer is, what it is?

**Exercise 3.3**Using the rules of taking a derivative, find the derivative of

**f(x) = √x+√x***Answer*

[

*]*

**1+1/(2√x)**

**/2√x+√x**

**Exercise 3.4**Using the rules of taking a derivative, find the derivative of

**f(x) = arctan(1/x)***Answer*

**−1/(1+x²)**

**Exercise 3.5**Using the rules of taking a derivative, find the derivative of

**f(x) = x**^{1/x}*Answer*

**x**^{1/x}·(1−ln(x))/x²

**Exercise 3.6**Using the rules of taking a derivative, find the derivative of this implicitly defined function

**y**^{x}= x^{y}(of course, the derivative will also be implicitly defined)

*Answer*

**(y²−x·y·ln(y))/(x²−x·y·ln(x))**
## No comments:

Post a Comment