using implicit differentiation and a point to find equation of the tangent line.

Quote:

Originally Posted by escreality

I've been struggling to work on this problem.

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
I know I differentiate the equation to get slope of the tangent, but I have no idea what to do afterwards, or frankly if my differentiation is even correct.

y sin 12x = x cos 2y, (pi/2, pi/4)

Any help is greatly appreciated.

$\frac{d}{dx} [y\sin(12x) = x\cos(2y)]$

product rule, both sides ...

$y \cdot 12\cos(12x) + y' \cdot \sin(12x) = -x\sin(2y) \cdot 2y' + \cos(2y)$

sub in $x = \frac{\pi}{2}$ and $y = \frac{\pi}{4}$ and solve for the value of $y'$ , the slope of the tangent line.

Write your tangent line equation.