what is the derivative of sec^2(3x) + tan^2(3x)?

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what is the derivative of sec^2(3x) + tan^2(3x)?

PLEASE HELP!!!

2006-10-22 10:59:23 · 2 answers · asked by Ben S 2 in Science & Mathematics ➔ Mathematics

2 answers

I tried it as well, the person above me is correct.

2006-10-22 11:35:13 · answer #1 · answered by Hadeer S 1 · 0⤊ 0⤋

Use the chain rule:

2*sec(3x)*d/dx(sec(3x)) + 2*tan(3x)*d/dx(tan(3x))
= 2*sec(3x)*(sec(3x)*tan(3x))*d/dx(3x) +
2*tan(3x)*sec^2(3x)*d/dx(3x)
= 12*sec^2(3x)*tan(3x).

Another way to do it is to recognize that sec^2 t = 1 + tan^2 t, and write the function as 1 + 2*tan^2(3x), and then differentiate.

2006-10-22 11:08:38 · answer #2 · answered by James L 5 · 0⤊ 0⤋