Question

Please help me with this calculus problem!

1.a) Differentiate each function:

i) (-pi/2)sin(20x-pi)
=10picos(20x)

ii) sin^2(cos^3(x)+tan(x)
=2cos(cos^3(x)+tan(x))(sin(cos^3(x)+tan(x))(sec^2(x)+3(-sin(x))cos^2(x))

iii) 4x^2sin^2(6x^2-2)
=4(2x)sin^2(2-6x^2)-24x^3sin(2-6x^2)cos(2-6x^2))

1.b) Determine f''(x) where f(x)=cot(4x) and f(x)=sin(x) times tan(x)
I need help with this one.

Answer 1

It looks like you have the answers. What are you asking?

Answer 2

For part b)

Answer 3

I dont know what to do

Answer 4

You have two different f(x) equations. You said f(x)=cot(4x) and f(x)=sin(x) not sure what you want with this. Do you want the second derivative of both?

Answer 5

f(x)=cot(4x)
f'(x) = - 4 csc² 4x

Answer 6

f (x) = sinx tanx
f'(x) = cosx tanx + sinx sec²x

Answer 7

Thanks for your help chlorophyll, its just that, I dont understand what the question is asking and what it has to do with part a)

Answer 8

All derivative f'(x)

Answer 9

Yes

Answer 10

So we're trying to find f''(x)?

Answer 11

f(x) = (-π/2)sin(20x-π)
f'(x) = 20 * (-π/2) cos (20x-π)
= -10 π cos (20 x - π )

Answer 12

So are those answers that I had wrong?

Answer 13

It seems not quite correctly!

Answer 14

I checked it with wolframalpha, hmm

Answer 15

sin² ( cos³ x+tanx )
Is it what you post?

Answer 16

yes

Answer 17

Have you checked wolf fram yet?

Answer 18

Yes, I checked them all with wolframalpha

Answer 19

It says you're right?

Answer 20

Yes

Answer 21

http://www.wolframalpha.com/input/?i=Differentiate+%28-pi%2F2%29sin%2820x-pi%29

Answer 22

http://www.wolframalpha.com/input/?i=Differentiate+sin%5E2%28cos%5E3%28x%29%2Btan%28x%29

Answer 23

http://www.wolframalpha.com/input/?i=Differentiate+4x%5E2sin%5E2%286x%5E2-2%29

Answer 24

Wolf has little bit different way calculation with manual one!

Answer 25

But is it still correct?

Answer 26

Not really, because there's couple of time I helped the askers, wolf answer different from their online solution, so they lost their points!

Answer 27

Ok disregarding that, how do we do part b)?

Answer 28

For example,
f(x) = (-π/2) sin (20x-π)
Let u = 20x - π
( sin u)' = u' cos u

Answer 29

I've already finished b part first o.o

Answer 30

it asks for f''(x) not f'(x)

Answer 31

so just take the next one!
f'(x) = - 4 csc² 4x
- 4 csc² (4x) = - 4 sin ^-2 ( 4x)
=> f" (x) = 32 sin ^-3 ( 4x) * cos (4x)

Answer 32

I was just wondering why is it part b) if it has nothing to do with part a)?

Answer 33

It's all individually questions, there's no related at all.

Answer 34

ok, thanks for your help :)