Simple derivative question

1. Jan 28, 2006

Chocolaty

What is the derivative of:
tan^4(3x)

The teacher wrote 4TAN^3(x) + sec^2(3x)(3) but i think he made a mistake.

I know that tan^4(3x) = tan(3x)^4 and that this equals 4tan(3x) in algebra
When I derive this i get the following: sec^2(3x)(3) i'm not sure what to do with the coefficient 4. Can someone give me the exact derivative formula to work this term out so I can copy it down plz.

thanks

2. Jan 28, 2006

Chocolaty

nevermind i got it. You need to use the generalized power rule:
[u(x)]^n => n*u^(n-1)*u'
so
tan(3x)^4 => 4*tan(3x)^3*sec^2(3x)(3)

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