Find the directional derivative of f at the given point in the direction indicated by the angle \theta. f(x,y)=e^x\cos y,(0,0),\theta=\frac{\pi}{4}

Sinead Mcgee 2021-05-19 Answered
Find the directional derivative of f at the given point in the direction indicated by the angle θ.f(x,y)=excosy,(0,0),θ=π4
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Expert Answer

Daphne Broadhurst
Answered 2021-05-20 Author has 109 answers
Jeffrey Jordon
Answered 2021-09-29 Author has 2027 answers

We need to find directional derivative of at the given point in the direction of v

f(x,y)=excosy; θ=π/4, (0,0)

Formula:

Duf(x,y)=fx(x,y)a+fy(x,y)b

Find partial derivatives

fx=excosy and fy=exsiny

Plug into formula

Duf=(excosy)cos(π/4)+(exsiny)sin(π/4)

=22[(excosy)+(exsin(y)]

Plug in values

22[e0cos0e0sin0]

Result: Duf(0,0)=22

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