Question

d/dt ( 2^(t)2sin^(-1)(2t+1)
derivatives.

Answer 1

@tkhunny please help!

Answer 2

Looks like a good "paying attention" problem. What have you tried?

This? \(\dfrac{d}{dt}2^{t}\cdot 2\cdot\sin^{-1}(2t+1)\)

Personally, I would rewrite it just a little. This? \(\dfrac{d}{dt}2^{t+1}\cdot\sin^{-1}(2t+1)\)

Answer 3

\[d/dt (2^t \sin ^{-1}(2t+1)\]

Answer 4

product rule and chain rule?

Answer 5

Okay, so no extra 2 and there is no need or temptation to rewrite it. Great.

You have the idea. Let's see what you get.

Hint: \(\dfrac{d}{dt}2^{t} = 2^{t}\cdot\log(2)\)

Answer 6

mmm i have no clue.

Answer 7

False. You had a clue a minute ago. Get it back.

Answer 8

ok,

Answer 9

chain rule for each numbers?

Answer 10

Hint: \(\dfrac{d}{dt}\sin^{-1}(t) = \dfrac{1}{\sqrt{1-t^{2}}}\)

That's about all you need.

Answer 11

Stop asking questions and start writing the derivative.

Answer 12

\(\dfrac{d}{dt}f(t)\cdot g(t) = f(t)\cdot g'(t) + g(t)\cdot f'(t)\) Go!

Answer 13

\[d/dt (2t+1)= (2)\]

Answer 14

That's part of it. Keep going.

Answer 15

product rules? but it does not make sense
\[2^t \sin^{-1} (2t+1) \]
three parts.
the product has two/ f(x)g(x)

Answer 16

@tkhunny

Answer 17

If there where three, you could just group them and make pairs.

There are only two.

\(2^{t}\)

\(\sin^{-1}(2t+1) = asin(2t+1)\)

Answer 18

oh.. i see.

Answer 19

\[2^t*(asin(2t+1)'+(asin(2t+1)(2^t)'\]
?

Answer 20

There's that question again. Move forward. Do NOT stop to ask every time you flinch! Keep going!

Answer 21

I want to make sure that i am doing right.
so i dont need to rise off all my effort and time writting wrong equation

Answer 22

Right. I understand your motivation. I am also telling you that it is holding you back. You have far too much fear. Learn the right things. Go the right direction. Go with confidence.

What's next?

Answer 23

\[(2^t)(1/\sqrt(1-t)*dx (2t+1)+asin(2t+1)(2^tlong(2)\]

Answer 24

So Close!!

\(\dfrac{d}{dt}asin(t) = \dfrac{1}{\sqrt{1-t^{2}}}\)

\(\dfrac{d}{dt}asin(2t+1) = \dfrac{1}{\sqrt{1-(2t+1)^{2}}}\cdot 2\)

Answer 25

See! That was very good. No need to fear. Just pay a little better attention.

Answer 26

\[2^t \frac{ 2 }{ \sqrt{1-(2t+1)}}+(\sin^{-1}(2t+1)(2^t* \log (2)) \]

Answer 27

Missed the "squared" in the square root. Otherwise, perfect.

Answer 28

sqrt(2t+1)?

Answer 29

Already showed you that. Pay better attention.

\(\dfrac{2}{\sqrt{1 - (2t+1)^{2}}}\)

Answer 30

ok, thank you

Answer 31

Now, seriously. This is where I look you in the eye and ask you if you are in the right class, if you are truly dedicated to this course, if you think you can gain the confidence to move forward - and various other questions about your mental health. Work hard. You'll get it!

Answer 32

Thank you very much tkhunny.
i will work hard and thank you for your advice.