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Study23

  • 3 years ago

It's the Chain Rule!

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  1. Study23
    • 3 years ago
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    \(\ \large \text{Find the derivative: } \) \(\ \Huge y=sin(tansinx^{\frac{1}{2}}).\)

  2. geerky42
    • 3 years ago
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    Yes, use chain rule.

  3. Study23
    • 3 years ago
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    How, though?

  4. geerky42
    • 3 years ago
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    Derivative outer function and left inner functions untouched, then derivative inner, left another inner functions untouched, then derivative inner-inner function, and so on. f(x) = sin x, g(x) = tan x, h(x) = sin x i(x) = √x, \(f(g(h(i(x)))) = sin(tan(sinx^{\frac{1}{2}})\) \[\frac{d}{dx} f(g(h(i(x)))) = f'(g(h(i(x)))) \cdot g'(h(i(x))) \cdot h'(i(x)) \cdot i'(x)\]

  5. Study23
    • 3 years ago
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    Thanks @geerky42!

  6. geerky42
    • 3 years ago
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    No problem.

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