Question

differentiate y=tan2 (x/3)
help me...

Answer 1

\[y = \tan^{2} (\frac{ x }{ 3 })\]

Answer 2

You have to use the chain rule twice.

Answer 3

First, let x/3=u

Answer 4

\[y=\tan^2u\]

Answer 5

Differentiate it like the following;\[\frac{ dy }{ dx }=\frac{ dy }{ du }*\frac{ du }{ dx }\]

Answer 6

\[\frac{ dy }{ du }=2\tan u \sec^2u\]

Answer 7

\[\frac{ du }{ dx }=\frac{ 1 }{ 3 }\]

Answer 8

Therefore, \[\frac{ dy }{ dx }=\frac{ 2 }{ 3 }\tan u \sec^2 u=\frac{ 2 }{ 3 }\tan \frac{ x }{ 3 } \sec^2 \frac{ x }{ 3 }\]

Answer 9

Oh, and my bad.
You only have to use the chain rule once, not twice.

Answer 10

Any questions?

Answer 11

okay!! thank u very much.