Given that $3x-tany=4$, what is $\frac{dy}{dx}$ in terms of $y$?

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.

y² = x² + 2x

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.

Given the equation $x{e}^y=x-y$, find $\frac{dy}{dx}$ using implicit differentiation.

In Exercises 27–32, find dy/dx.

ln y = e^y sinx

In Exercises 27–32, find dy/dx.

e^(2x)=sin(x+3y)

In Exercises 27–32, find dy/dx.

3+siny = y-x^3