Find dy/dx by implicit differentiation

Question

x³-tan ^-1y = e ^y

 

 

Please help guys!!

Answer 1

x³-tan ^-1y = e ^y

 

Differentiating implicitly: 3x² -y'/(1+y²) = y'e^y

 

y'(e^y+1/(1+y²) ) = -3x²

 

y' = -3x²(1+y²) / [1+e^y+y²e^y]

Answer 2

I THINK, if you get all the terms on one side (i.e., get a differentiable function = 0), then the derivative

 

dy/dx = -F_x/F_y,

 

where F_x is the derivative of F(x,y) with respect to the variable x (y terms being constant), F_y is the derivative of F(x,y) with respect to the variable y (x terms being constant).

 

 

That is definitely the rule. If I haven't messed up the application of the rule as stated, the derivative should be:

 

dy/dx= -3tan^-1y/[x((1/1+y2)-e^y)]

 

but check my derivative carefully.