Question

I need some help with a calculus question.

Find the derivitive of
f(x) = (1+cos^2x)^4
f(x) = sec^4(x)
f(x) = tan^4(x)

I have tried all of these and using chain rule, i have got answers, but the are not right. Someone please help me to figure these out with an explation.

Answer 1

sorry correction. the first one is f(x) = (1+cos^(2) (X))^4

Answer 2

show me what you came up with

Answer 3

4((1+cos^2(x))^3 * (-2sin(x)))
4(tan(x)/cos(x))
4(sec^2(x))^3

Respectively

Answer 4

(1+cos^2x)^4

i see 3 functions at play ( )^4 , ( )^2, and cos( )

4(1+cos^2x)^3 * (1+cos(^2x))'

4(1+cos^2x)^3 * 2(cos(x)) * (cos(x))'

4(1+cos^2x)^3 * 2(cos(x)) * (-sin(x))

Answer 5

the others are just 2 functions at play ...

4(f(x))^3 + f'(x)

Answer 6

not "+" but my fingers hate me lol

Answer 7

for the second two, do i not need to convert the trig function to the derivitive form?

Answer 8

you do, which is that the f' is in my general setup

tan' = sec^2

sec' = sec tan

Answer 9

i thought that was what i did? I'm sorry for being difficult, but i just dont see where i am going wrong with the sec problem.

Answer 10

sec^4(x)

(sec(x))^4

4(sec(x))^3 * (sec(x))'

4(sec(x))^3 * sec(x) tan(x)

Answer 11

or simply: 4 sec^4 tan

Answer 12

oh. i was looking at it as (x) was the inside not sec(x). Ok that makes a lot more sense now.

Answer 13

i find it a good idea to just rewrite those trig exponents in a more usual form :)

Answer 14

Ok that helps out a lot. Thanks for helping me with these proplems. Your explanations were great.

Answer 15

youre welcome, and good luck :)

Answer 16

Thanks!