Question

Find dy/dx by implicit differentiation.
3cos(8x)sin(4y)=3

Answer 1

hey

Answer 2

Differentiate both sides and solve for y':\begin{eqnarray*}&&\left(3\cos(8x)\sin(4y)\right)'=(3)' \\ \Rightarrow &&3\left(\left(\cos(8x)\right)'\sin(4y) + \cos(8x)\left(\sin(4y)\right)' \right) = 0\\\Rightarrow&&3\left( -8\sin(8x)\sin(4y) + 4\cos(8x)\cos(4y)y'\right) = 0\\\Rightarrow&&y' = 2\tan(8x)\tan(4y).\end{eqnarray*}

Answer 3

\[24\sin(8x)\sin(4y) + 12\cos(8x)\cos(4y)y'=0\] solve for
\[y'\]

Answer 4

krebante is right. i made a mistake the the first term should be
\[-24\sin(8x)\sin(4y)\] sorry.

Answer 5

hey thanks:) can u guys help me on another problem