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Double derivative of tan(x)

  • Thread starter _wolfgang_
  • Start date
  • #1
23
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Homework Statement


the question asked to prove that the double derivaitve of y=tan(x) is...
2y(1+y^2)
eg. 2tanx(1+tan^2(x))



Homework Equations





The Attempt at a Solution



I was able to get the first derivative ( i think)
y=tan(x)
=(sin(x))/(cos(x))

dy/dx=(cos(x)cos(x)-(sin(x)(-sin(x))))/cos^2(x)
=(cos^2(x)+sin^2(x))/cos^2(x)
=1/cos^2(x)

from here i am not to sure how to get the second derivative...
 

Answers and Replies

  • #2
Borek
Mentor
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2,681
So far so good, just differentiate cos-2x.
 
  • #3
23
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So would i use the quotient rule to do that or something else?? like the chain rule??
 
  • #4
23
0
ok iv done that i get
2sin(x)/cos^3(x)
now iv got the double derivative i cant see how to simplify it to get 2tanx(1+tan^2(x))
 
  • #5
Borek
Mentor
28,296
2,681
All I can tell is that

[tex]\frac {2 \sin x} {\cos^3 x} = \frac {2 \tan x } {\cos^2 x} [/tex]

is a correct second derivative.
 
  • #6
23
0
ok thanks for the help i should be able to get it from here
 

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