1. ## Implicit Differentiation

Find dy/dx by implicit differentiation

6(sin (8x))(cos (5y) = 4

I tried doing it and came up with

(tan (8x))(5 tan(5)), but this is not correct...

I tried doing it and came up with

(tan (8x))(5 tan(5)), but this is not correct...

Find dy/dx by implicit differentiation

6(sin (8x))(cos (5y) = 4
Applying the Product Rule and the Chain Rule, the differentiation would appear to start as:

. . . . .6*(8 cos(8x) (dx/dx))*cos(5y) + 6*(sin(8x))*(-5 cos(5y) sin(5y) (dy/dx)) = 0

. . . . .48 cos(8x) cos(5y) - 30 sin(8x) sin(5y) (dy/dx) = 0

. . . . .48 cos(8x) cos(5y) = 30 sin(8x) sin(5y) (dy/dx)

Divide through to isolate "dy/dx".

3. 8(tan8xtan5y) ?

4. Originally Posted by stapel

Applying the Product Rule and the Chain Rule, the differentiation would appear to start as:

. . . . .6*(8 cos(8x) (dx/dx))*cos(5y) + 6*(sin(8x))*(-5 cos(5y) sin(5y) (dy/dx)) = 0

. . . . .48 cos(8x) cos(5y) - 30 sin(8x) sin(5y) (dy/dx) = 0

. . . . .48 cos(8x) cos(5y) = 30 sin(8x) sin(5y) (dy/dx)

Divide through to isolate "dy/dx".
$\displaystyle \frac{dy}{dx} = \frac{48cos(8x)cos(5y)}{30sin(8x)sin(5y)} = \frac{8cot(8x)cot(5y)}{5}$