Question

Find the derivative of y=3tan^2 (x/3)

Answer 1

This is what I found on yahoo.

y = tan^2(x^3)
y'(incomplete) = 2 * tan(x^3)

Take care of trig function next.

y'(incomplete) = 2 * tan(x^3) * sec^2(x^3)

Take care of power function inside the trig function

y' = 2 * tan(x^3) * sec^2(x^3) * 3x^2
= 6x^2 * tan(x^3) * sec^2(x^3)

More elegant way?
f(x) = x^2, g(x) = tan(x), h(x) = x^3
y = f(g(h(x))) = tan^2(x^3)

Using chain rule

y' = f'(g(h(x)) * g'(h(x)) * h'(x)

f(x) = x^2, g(x) = tan(x), h(x) = x^3
f'(x) = 2x, g'(x) = sec^2(x), h'(x) = 3x^2

Substituting,

y' = f'(g(h(x)) * g'(h(x)) * h'(x)
= 2(tan(x^3)) * sec^2(x^3) * 3x^2
= 6x^2 * tan(x^3) * sec^2(x^3)

Answer 2

yea but my equation is different

Answer 3

can you derive each side of the problem?

Answer 4

i know you bring in the 2 to the font so it will be y=6tan(x/3) but idk what to do next

Answer 5

if the problem was
y= 3x^2
you would do
dy = 6x dx
in this case your "x" is tan(x^3)
so you would have
dy = 6tan(x^3) d tan(x^3)

in other words you know have to take the derivative of tan(x^3)

Answer 6

how do i do that ?

Answer 7

http://www.intmath.com/differentiation-transcendental/1-derivative-sine-cosine-tangent.php

Answer 8

sec^2x?

Answer 9

sec^2(stuff inside)

you started with tan(x^3)
so you would get
sec^2(x^3) d x^3
you now take the derivative of x^3

Answer 10

what happen to the 6?

Answer 11

all the other stuff is still there. I was just concentrating on the derivative part.
btw, is this the problem
y=3tan^2 (x/3) ?
(somehow x/3 turned into x^3)

to summarize,
d (y=3tan^2 (x/3) )
dy = 3 d tan^2 (x/3)

dy = 6 tan(x/3) d tan(x/3)
dy = 6 tan(x/3) sec^2(x/3) d x/3
dy = 6 tan(x/3) sec^2(x/3) ⅓ dx
dy = 3 tan(x/3) sec^2(x/3) dx
dy/dx = 2 tan(x/3) sec^2(x/3)

Answer 12

to summarize,
d (y=3tan^2 (x/3) )
dy = 3 d tan^2 (x/3)

dy = 6 tan(x/3) d tan(x/3)
dy = 6 tan(x/3) sec^2(x/3) d x/3
dy = 6 tan(x/3) sec^2(x/3) ⅓ dx
dy = 2 tan(x/3) sec^2(x/3) dx
dy/dx = 2 tan(x/3) sec^2(x/3)

Answer 13

is that it?

Answer 14

can you following the steps?

Answer 15

yes kinda

Answer 16

thank you

Answer 17

does the answer match any of your choices?

Answer 18

yes!:) thnxs