4. Compute all the partial derivatives of the following function (if they exist). a) R(p, q) = tan"'(pq²) b) f(x, y) = [" cos( d )dt c) g(x, y, z, t) = x²ycos(z/t) 1-Vx² +y² +z? 1+ Vx? +y² +z² d) f(x,y,z) = In -

Q: Find the partial derivative of z with respect to u if: 2=x+4y, x= u sin v, y=u cos v

A: Partial differentiation

Q: 1) Given f(x, y) = x derivative of f? which of the following is Əyox the mixed second order par f

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Q: What is the derivative of y = 3x²tan-1(x)?

A: ddxxn=n xn-1ddxtan-1x=11+x2 One have to use product rule here, which is ddx(uv)=vddxu+uddxv

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: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

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Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

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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: 2. Determine the directional derivative of o(x, y, z) = re" + y² + xyz at the point (2, 0, 3) in the…

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Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

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Q: Determine when the following pairs of functions are linearly independent. (a) y1(t) = e"it; Y2(t) =…

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Q: Let f(x, y, z) = x“y + z* and x = s³, y = st°, and z = s°t. (a) Calculate the primary derivatives ,…

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Q: 15. Differentiate 4y³ with respect to x. A) 12y? B) 12y C) 12y2 dy D) 4y2 dy dx dx 16-17. Find the…

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Q: Find the partial derivative of the function g(r,0) = r cos 0 + r sin 0.

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Q: Find the partial derivative of the function WIUI h(p.o.0) = p sin o cos 0

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Q: Let f(x, y) = x/y. Then the directional derivative of f in the direction of √2 point (1, 1) is ○ (1,…

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Q: 7. Which of the following sets of functions is linearly dependent on R0,2? (a) {6, z, sinz} (b) {1,…

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Q: Find the first order partial derivative with respect to y of the function f (x, y) = x³y² + 3æe".…

A: Differentiate given function with respect to y treat x as a constant.

Q: Suppose that the partial derivatives of a function ƒ(x, y, z) at points on the helix x = cos t, y =…

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Q: f(x, y, z) = x + tan(yz) exyz + 1

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Q: Use the Chain Rule to find the indicated partial derivatives. = x² + x²y, x = s +2tu, y = stu²; Z =…

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Q: What is the result of the partial derivative 3(z² + y sin (z)) Select one: a. 2a + y * cos(x)

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