Differentiation of Trigonometric functions

[MaxManus]

Homework Statement

Let y = tan²(3x-2)
Find dy/dx


The solution is:
2*tan(3x-2)*sec(3x-2)*3
= 6*tan(3x-2)*sec²(3x-2)

Why is it not:
6*tan(3x-2)*sec(3x-2)

I am thinking:
y = (tan(3x-2))²
take the power 2 down,multiply with the parentes multiply with the defferentiated parentes

Edit: Happy new year

 

[tiny-tim]

happy new year!

Let y = tan²(3x-2)
Find dy/dx
…
Why is it not:
6*tan(3x-2)*sec(3x-2)

I am thinking:
y = (tan(3x-2))²
take the power 2 down,multiply with the parentes multiply with the defferentiated parentes

Hi MaxManus! Happy new year!

(what are parentes? do you mean "parenthesis"?)

y = (thing)²,

so y' = 2(thing)(thing') …

in this case, the thing is a tan, and tan' = sec²

 

[jgens]

What do you think d(tan(u))/dx is equivalent to?

Edit: tiny-tim beat me to it.

 

[tiny-tim]

happy new year!

Edit: tiny-tim beat me to it.

na na na na-na!

hic!

happy new year! ​

 

[jgens]

Happy new year! :)

 

[MaxManus]

Thanks tiny-tim and jgens.
Yes, I ment parenthesis, but I could not spell it.

 

[HallsofIvy]

Hitting the champagne a little early?