1. Find the first order partial derivatives: 2= In (x+ 2. Find the gradient of the function f(r.y) = In(r² + y² ) at the point(1,1). 3. Find the derivative of the function f(r, y, 2) = ry + yz + 2r at the point (1.-1,2) in the direction A = 31 + 6j – 2k.

Q: Given F(r, s, t) = -r(58³ + 7tº), compute: Frst

A: Frst is a third order partial, where we differentiate first with respect to r, then with respect to…

Q: Find all the first and second order partial derivatives of f(x, y): = = 3x³y + 10xy². A. f = fx =…

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Q: 2. Find the gradient of the function f(x, y) = ln(x² + y²) at the point(1, 1).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: How to solve this equation y'''+2y''+4y'+8y=5e^(3t)+1 using Method of Undetermined Coefficient

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Q: Find the four second-order partial derivatives for: f(x, y) = 2x³y - 5xy + 7y

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Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y, x = s + 2t - u, y =: =…

A: Given the function z,x and y.

Q: Use the chain rule to find the indicated partial derivatives. x4. x² + x²y₁ x = s + 2t - u, y = stu…

A: To find partial derivatives of z w.r.t. s,t,u   Given z=x4+x2yx=s+2t-u and y=stu2

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 the partial derivatives .

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Q: Use the Chain Rule to find the indicated partial derivatives x = s + 2t - u, y = stu²; when s = 4, t…

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Q: Explain how a directional derivative is formed from the two partial derivatives f, and f,. Choose…

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Q: Use the chain rule to find the indicated partial derivative z = x4 + x²y, x = s + 2t - u, y = stu2…

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Q: Use the Chain Rule to calculate the partial derivatives д(т, у) — sin (т? + у?), х— 4и — v, у — —…

A: Given g(x, y)=sin(x2+y2) ,x= 4u-v and y=-(2u+2v)

Q: Compute the partial derivative fa (7,y, z) of the function f(2, y,z) = ?y yze(? u*+y*+x) + *ye(2…

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Q: Consider the function f(x,y)=4x°y+2x?-y? +3y-5. Calculate the partial derivative f,(1,2). Answer:

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