anonymous
  • anonymous
It's the Chain Rule!
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\(\ \large \text{Find the derivative: } \) \(\ \Huge y=sin(tansinx^{\frac{1}{2}}).\)
geerky42
  • geerky42
Yes, use chain rule.
anonymous
  • anonymous
How, though?

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geerky42
  • geerky42
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, \(f(g(h(i(x)))) = sin(tan(sinx^{\frac{1}{2}})\) \[\frac{d}{dx} f(g(h(i(x)))) = f'(g(h(i(x)))) \cdot g'(h(i(x))) \cdot h'(i(x)) \cdot i'(x)\]
anonymous
  • anonymous
Thanks @geerky42!
geerky42
  • geerky42
No problem.

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