Question

if y=square root(xsinx), derivative of this would be...?

Answer 1

\((\sqrt{x .\sin x})'=...\)
typical chain rule+product rule problem,
whats the derivative of \(\sqrt x \) ?

Answer 2

1/2(x)^-1/2

Answer 3

yes, so ,applying chain rule,
\((\sqrt{x .\sin x})'=...\)

Answer 4

op, got answeer ok
what about the 100th derivative of sin3x???

Answer 5

good!
whats 1st derivative ?

Answer 6

I think the answer is \[\sqrt{x}/2.cosx + \sqrt{sinx}/2\sqrt{x}\]

Answer 7

shrini, the answer is (xcosx+sinx)/2(xsinx)^-1/2
and the 1st derivative is sin3x is cos3x?

Answer 8

*ofsin3x

Answer 9

just cos 3x ?? or 3cos 3x ?

Answer 10

@lucy4104 I used the product rule and I got this. I don't know if I'm right.

Answer 11

(sin 3x)' = cos 3x *(3x)' = 3* cos 3x
using chain rule,
whats the 2nd derivative ?

Answer 12

did you use the chain rule, @hartnn ?
and I used the chain rule, shrini

Answer 13

yes.

Answer 14

@lucy4104 \[\sqrt{xsinx}=\sqrt{x}*\sqrt{sinx}\]
So, i used the product rule.

Answer 15

ok, I get how you got first derivative, so would the second be 9cos3x?

Answer 16

d/dx cos x = - sin x
so, d/dx (3 cos 3x) = 3 (-sin 3x) (d/dx 3x) = -9 sin 3x
ok ?

Answer 17

ok

Answer 18

and third derivative.... ?
the point is that we will find first few derivatives, then generalize it in terms of n'th derivative and then put n=100

Answer 19

ok

Answer 20

third deriv
-9sin3x----->-9cos3x*3----->-27cos3x

Answer 21

now lets generalize :
1st derivative : 3^1 cos 3x
2nd derivative : -3^2 sin 3x
3rd derivative : -3^3 cos 3x
4th derivative : +3^4 sin 3x
and so on.

Answer 22

so, for 'odd' derivative , we see cos 3x term, and for 'even' derivative, we see 'sin 3x'

Answer 23

and for n'th derivative, we see 3^n term,
clear so far ?

Answer 24

what about the negative?

Answer 25

yes,
after every 2 positive derivatives, comes 2 negative derivative...
or, can i say, 4th, 8th, 12th,.... 100th, 104th..... derivative will be positive, that is derivative which are multiples of 4 are positive... ?

Answer 26

that last part confuzzled me

Answer 27

try and figure out by yourself, whether 100th derivative will be positive or negative?

Answer 28

1st was pos, 2and 3 was neg, 4th and 5th was pos, 6and 7 was neg, 8 and 9 is pos, 10 and 11 is neg, 12 and 13 is pos, 14, 15 is neg, 16 and 17 is pos. oh I see 4, 8, 12, 16 are positive and then the one number after it is also positive.

Answer 29

good observation, what about 100th ?

Answer 30

with positive derivative and since 100 is even, we'll have sin 3x and term 3^100.
100th derivative of sin 3x will be 3^100 sin 3x

Answer 31

oh!!! ok thanx

Answer 32

welcome ^_^