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Differentiate sin(sin(sin x))

Mathematics
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i've done it by i want it checked
\[\frac{d}{dx}(\sin(\sin(\sin(x)) = \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x)\]
yup - thanx

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Other answers:

you're pretty fast - it took me a while to figure that out
How??
i used the chain rule
Always remember: \[\frac{d}{dx}(f(x)) = \frac{d}{dx}(f(x)) \times \frac{d}{dx}(x)\]
- maybe its because i'm not too keen on calculus lol
So \[\frac{d}{dx}(\sin(\sin(\sin(x)) = \cos(\sin(\sin(x))) \times \frac{d}{dx}(\sin(\sin(x))\] \[\cos(\sin(\sin(x))) \times \frac{d}{dx}(\sin(\sin(x)) \implies \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \frac{d}{dx}(\sin(x))\]
\[\cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \frac{d}{dx}(\sin(x)) = \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x) (1) \]
\[\cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x) \times \frac{d}{dx}(x)\] \[\implies \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x)\]
One by one we have to take all the derivative..
yes - i think i just need some practice in these to speed me up
ty
You are quite intelligent I believe.. Just a little more practice will give you command over this..
Welcome dear..

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