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| | | Module No. 5 Directional Derivative 0 determine the derivative in ific directi han the coordinate axes _ edure to determine t ivative in.a specific direction, other t eee (x, y,2) is called directional derivative. Ed See ee ic region on R and also differentiable Let p(x, y,z) be a scalar point function defined on a specifi ' e the rate of change of g in the on the same domain. The first partial derivatives of (x,y,z) ar ial a 4 2 is given direction of coordinate axes (x,y,z). It is a restricted way to calculate the rate change is g1V function. Maybe one ought to need the derivative in a specific direction. Therefore the idea of directional derivative introduced. To define the directional derivative we choose a point A(x,y, 2) in space and a direction at Py given by a unit vector a. Let C be the ray drawn from P in the direction of G, and let A(x + Ax,y + Ay,z + 4z) denoted by B be a neighboring point on C, whose distance from P is As as shown in figure, The value of given scalar point function is p(x, y,z) and p(+Ax,y + Ay, z+ dz) at P and P” respectively. Then the limit be, 900) MH As lim — = lim ds-0 As ds~0 ee if it exists, is called the directional derivative of g at P in the direction of @ and is denoted by ae. 7 as Obviously, 
