Chain Rule? find the derivative of sin(sin(sin(sin(sin(x)))))
- Thread starter Frenchi33
- Start date
- Joined
- Nov 24, 2012
- Messages
- 3,021
Let:
\(\displaystyle y=\sin\left(\sin\left(\sin\left(\sin\left( \sin(x)\right)\right)\right)\right)\)
Then by the rule for differentiating the sine function and the chain rule, we have:
\(\displaystyle \displaystyle \frac{dy}{dx}= \cos\left(\sin\left(\sin\left(\sin\left( \sin(x)\right)\right)\right)\right) \frac{d}{dx}\left(\sin\left(\sin\left(\sin\left( \sin(x)\right)\right)\right)\right)\)
Can you continue?
\(\displaystyle y=\sin\left(\sin\left(\sin\left(\sin\left( \sin(x)\right)\right)\right)\right)\)
Then by the rule for differentiating the sine function and the chain rule, we have:
\(\displaystyle \displaystyle \frac{dy}{dx}= \cos\left(\sin\left(\sin\left(\sin\left( \sin(x)\right)\right)\right)\right) \frac{d}{dx}\left(\sin\left(\sin\left(\sin\left( \sin(x)\right)\right)\right)\right)\)
Can you continue?