Simple derivatives, Mathematics

Simple derivatives

Example   Differentiate following.

 (5x3  - 7 x + 1)5 ,[ f ( x )]5 ,[ y ( x )]5

Solution: Here , with the first function we're being asked to do the given,

d  [(5x3  - 7 x + 1)5/ dx =  5 (5x3  - 7 x + 1)4 (15x2  - 7 )

and it is just the chain rule.  We differentiated the outside function (the exponent of 5) and then multiplied that by the derivative of the inside function (the stuff inside the parenthesis).

For the second function we're going to do basically the similar thing.  We're going to have to use the chain rule. Still the outside function is the exponent of 5 whereas the inside function this time is simply f ( x ) . We don't contain a particular function here, however that doesn't mean that we can't at least write down the chain rule for this function. Following is the derivative for this function,

d  [ f ( x )]5 / dx = 5 [ f ( x )]4 f ′ ( x )

Actually we don't know what f ( x ) is so while we do the derivative of the inside function all we can do is write down notation for the derivative, that means f ′ ( x ) .

Along with the final function here simply we replaced the f in the second function along with a y since most of our work in this section will involve y's rather than f's.  Outside of that this function is alike to the second. Thus, the derivative is,

d  [ y ( x )]5  = 5 [ y ( x )]4  y′ ( x )

Posted Date: 4/12/2013 3:57:10 AM | Location : United States

Related Discussions:- Simple derivatives, Assignment Help, Ask Question on Simple derivatives, Get Answer, Expert's Help, Simple derivatives Discussions

Write discussion on Simple derivatives
Your posts are moderated
Related Questions
Find out the least number of cables required to connect 100 computers to 20 printers to assurance that 20 computers can directly access 20 different printers.  Justify your answer.

Write following in terms of simpler logarithms.  (a) log 3 (9 x 4    / √y) Solution log 3 (9 x 4 / √y) =log ­ 3 9x 4 -  log  y (1/2) =log ­ 3 9 + log ­ 3 x 4

The top of the new rectangular Big Gig Thingamajig is 80 inches long and 62 inches wide. What is the top''s perimeter?

a computerized payroll package and its cost,futures and the size of the business and how business mathematics is an inbuilt component of the package

Sketch the graph of h (t ) = 1 - 5e  1/(t/2) Solution : Let's primary get a table of values for this function. Following is the sketch. The major point behin

solve for y given that 3sin^2 y+cos y-1=0 for 0y360

At a point in a loaded member, the stresses relative to an x, y, z coordinate system are given by Calculate the magnitude and direction of the maximum principal stress.

Universal set The term refers to the set which contains all the elements such an analyst wishes to study.  The notation U or ξ is usually used to denote universal sets.

Errors Are Useful :  While teaching children, you must have found theft making mistakes off and on. How do you respond to the errors'? What do they tell you about the child-failur