Question

Find the directional derivative of f(x,y)=e^(xsiny) at the point P(1,0) in the direction of Q(-2,4)

Answer 1

Partial w/ respect to x:
\[\sin y [e^(xsiny)]\]
evaluated at (1,0)=0
w/ repect to y:
\[x \cos y[e^(x \sin y)]\]
evaluated at (1,0)=1
\[D _{Q}f(1,0)=af _{x}+b f _{y}=(-2)(0)+(4)(1)=4\]
where a and b are the components of Q

Answer 2

thank you :)