Qualification > Revison Notes

Differentiating exponentials and logarithms

(1/5) > >>

nid404:
One of our members asked for help, so I thought of posting it up for the others to benefit as well :)

= +

= + +


=


If

same goes for derivative of  ln x

exponentials










=



= +

=

= ---> in this case is unit

=

since

=


Same goes for derivative of ln x






= +

=

=



==



lol...that sure took looong to type....I will solve some sample problems from my textbook--Pure mathematics 2&3 Hugh Neill and Douglas Quadling...in a while  ;)

nid404:
Ex 4 A of the textbook

Differentiate

I'm writing the numbers as per the textbook so the ones who use it find it easier to look for.

1)

a) e3x
= e3x

=e3xX3= 3e3x

h) 3e. e2+4x

=3e3+4x

= 3e3+4x
  
=  3e3+4xX 4

= 12e3+4x


nid404:
4)
c) y= e^
    y= e^ X
    y=  e^ X 0.5 (1-x2)-1/2 X 2x
    y= e^ - x (1-x2)-1/2

Saladin:
+ REP. Good job.

nid404:
hey thanks

Exercise 4 B

1)
j) dy/dx ln(x(x+1))

dy/dx ln (x2+x)

1/(x2+x) X d (x2+x)/dx

(2x+1)/ (x2+x)

4) b)

y= 0.5 ln (2+ x4)
  = 1/2 X 1/(2+ x4) X d(2+ x4)/dx
  =1/2 X 1/(2+ x4) X 4x3
  =  4x3/ 4+2x4
  =2x3/2+x4

Navigation

[0] Message Index

[#] Next page

Go to full version