Find the derivative of the curve to find the line slope at the given point
sqrt(xy) + 4 dy/dx = 39
0.5(xy)^(-0.5) * (y + x dy/dx) + 4dy/dx= 0
No need to amplify simply plug in the given point ( 1,9)
0.5 ( 1 * 9)^(-0.5)* ( 9 + dy/dx) + 4dy/dx = 0
Solve for dy/dx
1/6( 9 + dy/dx) = -4dy/dx
9 + dy/dx = -24 dy/dx
-25dy/dx = 9
dy/dx = -9/25
as your question implies , you know the rest of the steps.
