Let F = < 3(x + 2)², 3 cos(x) + yz — 36y, — (z − 6y)² + ey > . Calculate the divergence of F and - - find point P where div(F) = 0. P=

Q: Find the partial derivative fx and fy of the given function 3x f(x, y) = -y2 :/ cos(r? – - t + 1)dt.

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Q: Q3) for f(v) = sec2(3v – 1) and g(v) = tan?(3v – 1) show that %3D %3! f'(v) = g'(v).

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Q: IT ) Verify that ,0) is a critical point of f(x, y) = y² - 2y cos x. Then use the second derivative…

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Q: Following function f(x ,y) = x3 - 3x2y + 2y2 - 12 Verify that 2* d2f / dx2 + 2*d2f / dydx +…

A: f(x,y)=x3-3x2y+2y2-12formula used is(i)  ∂ ∂x(xn)=nxn-1 (ii)  ∂ ∂x(constnat)=0

Q: (A) Suppose C= 4x²y + i3x³y? . Find divergence of C.

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Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

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Q: Consider y=(x2+1)2x a) find dy/dx b)Evaluate y'(1)

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Q: Let f(x, y) = (x° + ay´, xʻy°, 2x+by), g(u,v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: f(x,y)=(x3+ay2,x2y3,2x+by)g(u,v,w)=(3u2+bv2+w3,uvw)To Find: Derivative of f(g(u,v,w)) using the…

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: Xyz f(x.y.z) = function is given dt P(2,t,) in point fax + fy + f2z colculate.

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Q: Compute the derivative for r(t) = d dt f(t) = (Use symbolic notation and fractions where needed.)…

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Q: what is of point Fyl-2,0) fexsy)=(x3ーy+g)s

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Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

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Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

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