# Differentiation/ find the derivative

1. $sin^2(cos3x^3)^5$
2. $cot^2(x)((x^2)(3cos^3(3x)))^2$
• Chain rule chain rule chain rule chain rule – user137794 Apr 24 '14 at 20:33
• i tried but i cannot get to the answer – Assab Amad Apr 24 '14 at 20:33
• Why would a teacher assign such a ridiculous question? – user142299 Apr 24 '14 at 20:33
• without proper parentheses, it is difficult to tell what is wanted, especially in the first question. – robjohn Apr 24 '14 at 20:52
• I would propose to check this and this. You can create a free trial account to see the proof... – moray95 Apr 24 '14 at 21:37

\begin{align} \frac{d}{dx}\sin^2(\cos3x^3)^5&=2\sin(\cos3x^3)^5\cdot\frac{d}{dx}\sin(\cos3x^3)^5\\ &=2\sin(\cos3x^3)^5\cdot\cos(\cos3x^3)^5\cdot\frac{d}{dx}(\cos3x^3)^5\\ &=2\sin(\cos3x^3)^5\cdot\cos(\cos3x^3)^5\cdot5(\cos3x^3)^4\cdot\frac{d}{dx}\cos3x^3\\ &=who\ the\ hell\ made\ you\ do\ this \end{align}
• Run out of breath ? = $-2\sin(\cos3x^3)^5\cdot\cos(\cos3x^3)^5\cdot5(\cos3x^3)^4\cdot 9x^2\cdot\sin3x^3\\$ – Tom Collinge Apr 24 '14 at 20:47