Find the derivative of \(y=2 \sin \left(2 x^3+3 x-4\right)\)
A. \(2 \cos \left(2 x^3+3 x-4\right)\)
B. \(\left(6 x^2+3\right)\) cost \(\left(2 x^3+3 x-\right.\)
C. \(2 \sin \left(2 x^3+3 x-4\right)+2\)
D. \(\left(6 x^2+3\right)\left(2 x^3+\right.\) \(3 x-4)\)
Correct Answer: B
Explanation
\(y=2 \sin \left(2 x^3+3 x-4\right)\)
let \(\mathrm{u}=2 x^3+3 x-4, \frac{d x}{d x}=6 x^2+3\)
\(y=2 \sin u, \frac{d y}{d u}=2 \cos u=2 \cos \left(2 x^3+3 x-4\right)\)
\(\frac{d y}{d x}=\frac{d y}{d u} \times \frac{d u}{d x}=2 \cos \left(2 x^3+3 x-4\right) \times 6 x+3\)
\(=2\left(6 x^2+3\right) \cos \left(2 x^3+3 x-4\right)\)