Find the directional derivative of F = x²yz³

Answered question

2022-05-10

Find the directional derivative of F = x²yz³ along the curve x = e^-u, y= 2sinu + 1 ,z = - cosu at the point P where u = 0

Answer & Explanation

nick1337

nick1337

Expert2022-08-10Added 777 answers

F=x2y z3 

 FJJx F i^ +JJy j +JJzk^

 F  2xy z3 i^+x2 z3 j ^ +3x2 y z2 k^

Where,

x=e-u

y=2 sinu+1

z=u-cosu

at u=0

x=1,   y=1,    z=-1

F  -2i^ -j^+3k^

D·D= F · AB^

Unit vector along the curve 

i^+j^-k^12+12+-12

i^+j^-k^3

D·D  -2i^-j^+3k^·i^+j^-k^3

 13-2-1-3

-73

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