Question

Consider the curve given by 2^y x + y^3 = 1 . Find dy/dx

Answer 1

dy/dx= - ( 2^xy log(2)y )/3y^2

1.Given equation is 2^xy+y^3=1.

2. Let differentiate on both sides

above equation with respect to x.

3. d/dx (2^xy)+d/dx(y^3)=d/dx(1)

4. 2^xy log(2)y + 3y^2 dy/dx=0

5. dy/dx= - ( 2^xy log(2)y )/3y^2