## Dodo1 2 years ago d/dt ( 2^(t)2sin^(-1)(2t+1) derivatives.

1. Dodo1

2. tkhunny

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

3. Dodo1

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

4. Dodo1

product rule and chain rule?

5. tkhunny

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

6. Dodo1

mmm i have no clue.

7. tkhunny

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

8. Dodo1

ok,

9. Dodo1

chain rule for each numbers?

10. tkhunny

Hint: $$\dfrac{d}{dt}\sin^{-1}(t) = \dfrac{1}{\sqrt{1-t^{2}}}$$ That's about all you need.

11. tkhunny

Stop asking questions and start writing the derivative.

12. tkhunny

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

13. Dodo1

$d/dt (2t+1)= (2)$

14. tkhunny

That's part of it. Keep going.

15. Dodo1

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

16. Dodo1

@tkhunny

17. tkhunny

If there where three, you could just group them and make pairs. There are only two. $$2^{t}$$ $$\sin^{-1}(2t+1) = asin(2t+1)$$

18. Dodo1

oh.. i see.

19. Dodo1

$2^t*(asin(2t+1)'+(asin(2t+1)(2^t)'$ ?

20. tkhunny

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

21. Dodo1

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

22. tkhunny

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?

23. Dodo1

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

24. tkhunny

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

25. tkhunny

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

26. Dodo1

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

27. tkhunny

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

28. Dodo1

sqrt(2t+1)?

29. tkhunny

Already showed you that. Pay better attention. $$\dfrac{2}{\sqrt{1 - (2t+1)^{2}}}$$

30. Dodo1

ok, thank you

31. tkhunny

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!

32. Dodo1

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