Question

Differentiate sin(sin(sin x))

Answer 1

i've done it by i want it checked

Answer 2

\[\frac{d}{dx}(\sin(\sin(\sin(x)) = \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x)\]

Answer 3

yup - thanx

Answer 4

you're pretty fast - it took me a while to figure that out

Answer 5

How??

Answer 6

i used the chain rule

Answer 7

Always remember:

\[\frac{d}{dx}(f(x)) = \frac{d}{dx}(f(x)) \times \frac{d}{dx}(x)\]

Answer 8

- maybe its because i'm not too keen on calculus lol

Answer 9

So

\[\frac{d}{dx}(\sin(\sin(\sin(x)) = \cos(\sin(\sin(x))) \times \frac{d}{dx}(\sin(\sin(x))\]

\[\cos(\sin(\sin(x))) \times \frac{d}{dx}(\sin(\sin(x)) \implies \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \frac{d}{dx}(\sin(x))\]

Answer 10

\[\cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \frac{d}{dx}(\sin(x)) = \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x) (1) \]

Answer 11

\[\cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x) \times \frac{d}{dx}(x)\]

\[\implies \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x)\]

Answer 12

One by one we have to take all the derivative..

Answer 13

yes - i think i just need some practice in these to speed me up

Answer 14

ty

Answer 15

You are quite intelligent I believe..
Just a little more practice will give you command over this..

Answer 16

Welcome dear..