Answer to Question #105949 in Mechanics | Relativity for Vishal Kumar

Question #105949
Obtain the directional derivative for a scalar field phi( X,Y,Z)= 3x^2y-y^3z^2 at the points (1,-2,-1) in the direction i+j+k
1
Expert's answer
2020-03-23T10:35:22-0400

directional derivative is

"\\vec{A}=\\nabla\\phi=\\frac{\u2202 \\phi}{\u2202x}i+\\frac{\u2202 \\phi}{\u2202y}j+\\frac{\u2202 \\phi}{\u2202z}k"

then

"\\frac{\u2202 \\phi}{\u2202x}=6xy=-12"

"\\frac{\u2202 \\phi}{\u2202y}=3x^2-3y^2z^2=3-12=-9"

"\\frac{\u2202 \\phi}{\u2202z}=2y^3z=16"

Answer


"\\vec{A}=12i-9j+16k"


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