SOLUTION: Please explain how to solve using implicit differentiation. {{{ e^(xy)=4x+4y+20 }}} Thank you

Algebra.Com
Question 992887: Please explain how to solve using implicit differentiation.

Thank you

Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
Please explain how to solve using implicit differentiation.


-------------------------------------------------------------

Take the differential of both sides.  Use the rule of taking the differential of a composite function and taking the differential of a product:

= ,

= .

Next,  express  dy  via  dx  in the form   dy = g*dy,   where  g  is a function of  x  and  y.

Then    = .


RELATED QUESTIONS

Let {{{ e^(xy) = 4x+4y+20 }}} Use implicit differentiation to find the derivative of y (answered by Fombitz)
Use implicit differentiation to find dy/dx: e^xy- ex^3 =... (answered by venugopalramana)
Can someone please show how to take the implicit differentiation of this problem?... (answered by Fombitz)
Please find dy/dx using implicit differentiation: y^2+e^y=ln x^2+4... (answered by funmath)
Hello good friends . I have an implicit differentiation question if someone could please... (answered by stanbon,Fombitz)
Find dy/dx by implicit differentiation, where 4x^6+3x^4y-4xy^6=6. dy/dx=? (answered by solver91311,ikleyn)
what is the solution to: implicit differentiation e^x + e^y =... (answered by MaartenRU)
Can you help me with this problem? Solve by means of implicit differentiation: (e^x)... (answered by solver91311,rothauserc)
Use implicit differentiation to find dy/dx: e^y lnx+ xy3=... (answered by venugopalramana)