# Implicit differentiation

• February 7th 2010, 12:27 AM
Bryn
Implicit differentiation
Hi,

I have the following equation:

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

After differentiating I get:

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

And with this, I need to work out dy/dx at (0,0)

When I try this it seems messy and I get zero. Can someone explain where I have gone wrong please

Many thanks
• February 7th 2010, 01:18 AM
Sudharaka
Quote:

Originally Posted by Bryn
Hi,

I have the following equation:

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

After differentiating I get:

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

And with this, I need to work out dy/dx at (0,0)

When I try this it seems messy and I get zero. Can someone explain where I have gone wrong please

Many thanks

Dear Bryn,

Note that the equation, $ln(8y)+6xy=ln(sin(4x))$ is not defined when y=o since ln(0) is not defined. Therefore you cannot find $\frac{dy}{dx}$ at (0,0)