JEE Main & Advanced Mathematics Differentiation Higher Partial Derivatives

Higher Partial Derivatives

Category : JEE Main & Advanced

 

 Let \[f(x,\,y)\] be a function of two variables such that \[\frac{\partial f}{\partial x},\frac{\partial f}{\partial y}\] both exist.

 

 

(1) The partial derivative of \[\frac{\partial f}{\partial y}\] w.r.t. \['x'\] is denoted by \[\frac{{{\partial }^{2}}f}{\partial {{x}^{2}}}\text{ }\]or \[{{f}_{xx}}\].

 

 

(2) The partial derivative of \[\frac{\partial f}{\partial y}\] w.r.t. \['y'\] is denoted by \[\frac{{{\partial }^{2}}f}{\partial {{y}^{2}}}\] or \[{{f}_{yy}}\].

 

 

(3) The partial derivative of \[\frac{\partial f}{\partial x}\] w.r.t. \['y'\] is denoted by \[\frac{{{\partial }^{2}}f}{\partial y\,\partial x}\] or \[{{f}_{xy}}\].

 

 

(4) The partial derivative of \[\frac{\partial f}{\partial y}\] w.r.t. \[x\] is denoted by \[\frac{{{\partial }^{2}}f}{\partial y\partial x}\] or \[{{f}_{yx}}\]. These four are second order partial derivatives.

 

 

Note : If \[f(x,\,y)\] possesses continuous partial derivatives then in all ordinary cases. \[\frac{{{\partial }^{2}}f}{\partial x\,\partial y}=\frac{{{\partial }^{2}}f}{\partial y\,\partial x}\] or \[{{f}_{xy}}={{f}_{yx}}\].



LIMITED OFFER HURRY UP! OFFER AVAILABLE ON ALL MATERIAL TILL TODAY ONLY!

You need to login to perform this action.
You will be redirected in 3 sec spinner

Free
Videos