Thursday, January 14, 2016

Calculate f'(x) if f(x)=ln[(5x+7)/(5x+3)] x>0 .

Because f(x) contains the logarithm of a quotient, we'll
apply the quotient rule:


ln(f/g)=ln f -ln
g.


ln[(5x+7)/(5x+3)] = ln(5x+7) - ln
(5x+3)


f'(x) = [ln(5x+7) - ln
(5x+3)]'


f'(x) = [ln(5x+7)]' -  [ln
(5x+3)]'


f'(x)= (5x+7)'/(5x+7) -
(5x+3)'/(5x+3)


f'(x) = 5/(5x+7) -
5/(5x+3)


We'll
factorize:


f'(x) = 5*[1/(5x+7) -
1/(5x+3)]


f'(x) =
5(5x+3-5x-7)/(5x+7)(5x+3)


f'(x) =
-20/(5x+7)(5x+3)

No comments:

Post a Comment

Comment on the setting and character of "The Fall of the House of Usher."How does setting act as a character?

Excellent observation, as it identifies how the settings of Poe's stories reflect the characters of their protagonists. Whet...