The Derivatives of Basic Functions

At some point in all of our mathematic careers, we need to buckle down and just MEMORIZE the derivatives of basic functions. This is the case with any function that is "elementary" (not part of a combination with other functions). Such functions include things like sin(x), ln(x), arctan(x), ax, 1/x, and cosh(x). A comprehensive list of these functions, with their derivatives, appears below:

More Information

The site below will help to explain the table above:

When you have successfully memorized all of the derivatives of basic functions, treat yourself to the video below. You, like the boy in the video, can now appreciate the beauty of the derivative!

Go to the following link to take a fun, interactive quiz on basic derivatives (an applet): 

Warning: it is extreeeeeemely easy. Take this interactive quiz before attempting the harder (haha) problems below. ENJOY!

http://www.svgs.k12.va.us/math/Derivatives/Dx%5EnQuiz.html

Review Problems

 1) Let y = ln(3) + e^6x   

     Find y¹

2) Let y = cotx + cscx – 5x 

     Find y¹

3) Let y = log₄x – coshx + 193 

     Find y¹

Answers:

1) y¹ = 6e^6x

²⁾ y¹ = -csc²x – cscxcotx – 5

3) y¹ = (1/x)(1/ln4) – sinhx  

A few simple multiple choice practice problems 

1) The derivative of the function y = 5 is:

a)      5

b)      5x

c)      5^x

d)      0

e)      x⁵

2) The derivative of the function y = sinx + cosx + secx + tanx is:

            a) cosx – sinx + sec²x - tanx

            b) sin²x + sinx - cscxcotx

            c) cosx

            d) sinx + cosx + secx + tanx

            e) cosx – sinx + secxtanx + sec²x

3) The derivative of the function y = 12x + e^3x

            a) 12 + e

            b) 12 + 3e^3x

                c) 12x

            d) e

            e) 36x + e^x

Answers:

1)      d

2)      e

3)      b