Question 923796
I would probably rewrite it as *[tex \large 27 \sin^9  (2x^4 + 1)] to make the differentiation simpler and less likely to make mistakes. Recall *[tex \large \sin^a \theta = (\sin \theta)^a].


The derivative is


*[tex \large 27 \cdot 9 \sin^8 (2x^4 + 1) \cdot \frac{d}{dx} \sin (2x^4 + 1)]


*[tex \large = 243 \sin^8 (2x^4 + 1) \cdot \cos (2x^4 + 1) \cdot 8x^3]


*[tex \large = 1944x^3 \sin^8 (2x^4 + 1) \cos (2x^4 + 1)]