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243144 - Fu(a,b = grad f(a,b*u……grad f(a,b*u =fx(a,b*u1...

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14.4 Directional Derivative: fu(a,b) = (f(a+hu1, b+hu2)-f(a,b))/h Calculat DD using grad vect. Grad f(a,b) = fx(a,b)i+fy(a,b)j F(x,y)=x^3y+3y+x..Find grad f(x,y). Find grad f(1,0). Fx = 3x^2y+1…….Fy = x^3+3 Grad f = (3x^2y+1)I +(x^3+3)j…PLUG in X and Y Grad f(1,0) = i+4j ( which is a vector) Th: f(x,y) differentiable @(a,b) and u=unit v, u=u1i+u2j

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Unformatted text preview: Fu (a,b) = grad f(a,b)*u……grad f(a,b)*u =fx(a,b)*u1+fy(a,b)*u2 U = 1/(SQ(2))*(i+j), ….f(x,y) = x^2+y^2 and fu (1,0) Use grad f(x,y) =2xi +2yj…. .grad f(1,0) = 2i Fu(1,0) = 2i*u ===2*1/((SQ(2))===SQRT(2) Find grad…….z = (x+y)e^y….Zx=e^y…and Zy = xe^y+e^y+ye^y SO Z = Zxi+Zyj………Z = e^yi+(xe^y+e^y+ye^y)...
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