# implicit differentiation

• Feb 6th 2010, 10:22 AM
Bryn
implicit differentiation
Hi,

Can anyone explain how I can find dy/dx of the following:[

8Ye^(6XY)]=sin(4x)

Many thanks

Bryn
• Feb 6th 2010, 10:40 AM
songoku
Hi Bryn

$8y~e^{6xy} = \sin(4x)$

$\ln (8y~e^{6xy}) =\ln \sin(4x)$

$\ln(8y)+6xy=\ln \sin(4x)$

Now do the implicit differentiation
• Feb 6th 2010, 12:09 PM
Bryn
I can't seem to proceed easily,

The answer I have worked out is as follows:

(1/8y)(dy/dx)+6y+6x*(dy/dx)=(4cos(4x))/sin(4x)

Using this the question asks me to find the value of dy/dx at the coordinates (0,0).

I found this to be 0 which it seems is wrong, can someone explain to me why this is?

Many thanks