Extension: Directional Derivatives
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Problems 7
- Find the directional derivative Duf(x,y)D_uf(x,y)Duf(x,y) if f(x,y)=2x3−5xy+3y2f(x,y)=2x^3-5xy+3y^2f(x,y)=2x3−5xy+3y2 and u\bf{u}u is the unit vector given by the angle θ=π3\th…
- Find the directional derivative Duf(x,y)D_uf(x,y)Duf(x,y) if f(x,y)=3x−5yf(x,y)=\sqrt{3x-5y}f(x,y)=3x−5y and u\bf{u}u is the unit vector given by the angle θ=−π6\theta=-\frac{…
- Find the directional derivative Duf(x,y,z)D_uf(x,y,z)Duf(x,y,z) if f(x,y,z)=yz−xf(x,y,z)=\frac{y}{z-x}f(x,y,z)=z−xy and v=<2,2,1>\textbf{v}=<2,2,1>v=<2,2,1> and u\bf{u}u is th…
- Find the directional derivative Duf(x,y)D_uf(x,y)Duf(x,y) if f(x,y)=2+3xyf(x,y)=2+3x\sqrt yf(x,y)=2+3xy and v=<4,−2>\textbf{v}=<4,-2>v=<4,−2>. What is Duf(4,5)D_uf(4,5)Duf(4,5)?
- Find the directional derivative Duf(x,y)D_uf(x,y)Duf(x,y) if f(x,y)=ln(x2+y3)f(x,y)=\ln(x^2+y^3)f(x,y)=ln(x2+y3) and v=<3,4>\textbf{v}=<3,4>v=<3,4>. What is Duf(6,2)D_uf(6,2)D…
- Find aaa if Du(3,1)=4D_u(3,1)=4Du(3,1)=4 for f(x,y)=axeyf(x,y)=axe^yf(x,y)=axey and v=<−2,2>\textbf{v}=<-2,2>v=<−2,2>.
- Find aaa (to the nearest whole number) if Du(1,2)=9.11D_u(1,2)=9.11Du(1,2)=9.11 for f(x,y)=x2+4xy−y2f(x,y)=x^2+4xy-y^2f(x,y)=x2+4xy−y2 and v=<a,1>\textbf{v}=<a,1>v=<a,1>.