# Function estimated with differential

• Apr 27th 2009, 09:28 PM
Frostking
Function estimated with differential
I just have a basic question but it is making it impossible to finish several problems.

When you use the differential of a function(x,y), the partial derivative with respect to x times change in x + partial derivative with respect to y times change in y to estimate the value of a function,

do you add both of these terms to the original function or do you subtract them??? I think from looking at formula used for a tangent line approximation, you would add them but my book does not cover this and I am not sure. Thanks again for answering such a basic question. Frostking
• Apr 27th 2009, 09:57 PM
CaptainBlack
Quote:

Originally Posted by Frostking
I just have a basic question but it is making it impossible to finish several problems.

When you use the differential of a function(x,y), the partial derivative with respect to x times change in x + partial derivative with respect to y times change in y to estimate the value of a function,

do you add both of these terms to the original function or do you subtract them??? I think from looking at formula used for a tangent line approximation, you would add them but my book does not cover this and I am not sure. Thanks again for answering such a basic question. Frostking

$\displaystyle f(x+\delta x,y+\delta y)\approx f(x,y)+\frac{\partial f}{\partial x}(x,y)~ \delta x+\frac{\partial f}{\partial y}(x,y)~ \delta y + ..$

CB