Question

Compute the derivative of cos(sqrt(x)) , with respect to x from first principle.

Answer 1

@experimentX @Mashy

Answer 2

it would be \[-1/2 \sin x\]

Answer 3

I am not 100 percent sure

Answer 4

isnt the derivative of cos(sqrt(x)) = -sin(sqrt(x))/2sqrt(x)

Answer 5

yea that seems right

Answer 6

i believe so @ton12

Answer 7

y u asking if you know lol

Answer 8

But Hw do u Figure out with 1st principle it is getting werid with that

Answer 9

\[-1/2 x ^{-1/2}\sin \sqrt{x}\]

Answer 10

i want to figure out it from 1st principle @aajugdar

Answer 11

uh well
differentiate root x
then differentiate sin root x
then multiply

Answer 12

chain rule

Answer 13

What is first principle?

Answer 14

lim h--->0 ( f(x+h) - f(x) ) / h

Answer 15

oh lol
okay
lets see

Answer 16

Lt h->0 [cos (√(x+h) - cos √x) ]/h = - 1/h *2 * sin (√x+h +√x) /2 sin (√(x+h) -√x)/2

= - (2sin √x) lt h-->0 1/h *sin (h/2 ((√x+h +√x) ) = - (2sin √x) * sin (h/2 ((√x+h +√x) )
----------------------------------------…
2 ((√x+h +√x) * (h/2 ((√x+h +√x) )
- (2sin √x) * 1/(2* 2√x) * 1 = -1/2√x * sin √x

Answer 17

try to get it
lol

Answer 18

http://www.meritnation.com/discuss/question/1757465

Answer 19

check on the site
you will understand

Answer 20

thxx buddy

Answer 21

you are welcome :)