Question

Find dyldx.
3. y=2x sin(3x)

Answer 1

`\large\boxed{(dy)/(dx)=2\sin(3x)+6\cos(3x)}`

Explanation:

`(dy)/(dx)=(2x\sin(3x))'\\\\\text{use}\ \bigg(g(x)\cdot f(x)\bigg)'=g'(c)f(x)+g(x)f'(x)\\\\\text{and}\ \bigg(f(g(x))\bigg)'=f'(g(x))\cdot g'(x)\\\\(dy)/(dx)=(2x)'(\sin(3x))+(2x)(\sin(3x))'\\\\(dy)/(dx)=2\sin(3x)+(2x)(\cos(3x)\cdot(3x)')\\\\(dy)/(dx)=2\sin(3x)+2x\cos(3x)\cdot3\\\\(dy)/(dx)=2\sin(3x)+6\cos(3x)`