## cwrw238 3 years ago Differentiate sin(sin(sin x))

1. cwrw238

i've done it by i want it checked

2. waterineyes

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

3. cwrw238

yup - thanx

4. cwrw238

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

5. waterineyes

How??

6. cwrw238

i used the chain rule

7. waterineyes

Always remember: $\frac{d}{dx}(f(x)) = \frac{d}{dx}(f(x)) \times \frac{d}{dx}(x)$

8. cwrw238

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

9. waterineyes

So $\frac{d}{dx}(\sin(\sin(\sin(x)) = \cos(\sin(\sin(x))) \times \frac{d}{dx}(\sin(\sin(x))$ $\cos(\sin(\sin(x))) \times \frac{d}{dx}(\sin(\sin(x)) \implies \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \frac{d}{dx}(\sin(x))$

10. waterineyes

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

11. waterineyes

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

12. waterineyes

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

13. cwrw238

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

14. cwrw238

ty

15. waterineyes

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

16. waterineyes

Welcome dear..