Mumbai university > Electronics and telecommunication engineering, Electronics engineering > Sem 3 > Applied mathematics 3

Marks : 04

Years : DEC 2015

Directional Derivative $=\dfrac {\bigtriangledown \phi.\bar a}{|\bar a|} \\ \bigtriangledown \phi =\bar i\dfrac {d\phi}{dx} + \bar j\dfrac {d\phi}{dy} + \bar k \dfrac {d\phi}{dz} =\bar i[4z^3-6xy^2z]+\bar j[-6x^2yz] + \bar k[12xz^2-3x^2y^2]\\ \triangledown \phi (2,-1,2) = 8\bar i +48\bar j + 84\bar k =4(2\bar i+12\bar j +21 \bar k) \\ \bar a =2\bar i+3\bar j+6\bar k ,|\bar a|=\sqrt{4+9+36}=7 \\ D.D =\dfrac {4(2\bar i +12\bar j + 21\bar k).(2\bar i +3\bar j + 6\bar k)}7 =\dfrac 47 [4+36+126] \\ =\dfrac {4\times 166}7 =\dfrac {664}7$