How to Find the directional derivative of?:

Question

#f(x,y)=e^(-xy), P(1,-1),v=-i+sqrt(3)#

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Answer 1 · 2018-05-01T10:22:23

#=e/sqrt2 (sqrt3 + 1)#

If the function #f( mathbf x)# is differentiable at #mathbf x_o#, then the directional derivative exists along any vector #mathbf v#, and is:

# nabla _(\mathbf {v} ) f( mathbf x_o )= nabla f( mathbf x_o )\cdot mathbf v #

You're looking at:

#nabla f(x,y)_P * langle sqrt3, -1rangle/2#

#=langle -ye^(-xy) , - x e^(-xy) rangle_P * langle sqrt3, -1rangle/2#

#=langle e , - e rangle * langle sqrt3, -1rangle/2#

#=e/sqrt2 (sqrt3 + 1)#