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cwrw238

  • 3 years ago

Differentiate sin(sin(sin x))

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  1. cwrw238
    • 3 years ago
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    i've done it by i want it checked

  2. waterineyes
    • 3 years ago
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    \[\frac{d}{dx}(\sin(\sin(\sin(x)) = \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x)\]

  3. cwrw238
    • 3 years ago
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    yup - thanx

  4. cwrw238
    • 3 years ago
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    you're pretty fast - it took me a while to figure that out

  5. waterineyes
    • 3 years ago
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    How??

  6. cwrw238
    • 3 years ago
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    i used the chain rule

  7. waterineyes
    • 3 years ago
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    Always remember: \[\frac{d}{dx}(f(x)) = \frac{d}{dx}(f(x)) \times \frac{d}{dx}(x)\]

  8. cwrw238
    • 3 years ago
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    - maybe its because i'm not too keen on calculus lol

  9. waterineyes
    • 3 years ago
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    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
    • 3 years ago
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    \[\cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \frac{d}{dx}(\sin(x)) = \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x) (1) \]

  11. waterineyes
    • 3 years ago
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    \[\cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x) \times \frac{d}{dx}(x)\] \[\implies \cos(\sin(\sin(x))) \times \cos(\sin(x)) \times \cos(x)\]

  12. waterineyes
    • 3 years ago
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    One by one we have to take all the derivative..

  13. cwrw238
    • 3 years ago
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    yes - i think i just need some practice in these to speed me up

  14. cwrw238
    • 3 years ago
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    ty

  15. waterineyes
    • 3 years ago
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    You are quite intelligent I believe.. Just a little more practice will give you command over this..

  16. waterineyes
    • 3 years ago
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    Welcome dear..

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