Find $dy/dx$ for the equation below using implicit differentiation.
$5x^2+y^3=12$

Second Derivatives

In Exercises 19–26, use implicit differentiation to find dy/dx and then d²y/dx². Write the solutions in terms of x and y only.

3 + sin y = y – x³

In Exercises 29 and 30, find the slope of the curve at the given points.

(x² + y²)² = (x – y)² at (1,0) and (1,–1)

Normal lines parallel to a line Find the normal lines to the curve xy + 2x – y = 0 that are parallel to the line 2x + y = 0.

Find $dy/dx$ for the equation below using implicit differentiation.

$3\sqrt{y}=x-y$

Find $dy/dx$ for the equation below using implicit differentiation.

$xy=\sin\left(y\right)$

66–71. Higher-order derivatives Find and simplify y''.

x + sin y = y

5–8. Calculate dy/dx using implicit differentiation.

x = y²

5–8. Calculate dy/dx using implicit differentiation.

sin y+2 = x