Find the derivative of the function f(x, y) =x2 + xy+ y at the point (-5,-4) in the direction in which the function increases most rapidly. O 32 O V455 O V461 O N365

Q: Find the derivative of the function. h(t) = (t + 3)2/3(3t2 − 5)3

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Q: Find the derivative of the function f(x,y,z) = In (xy + yz + zx) at the point (- 8, - 16, - 24) in…

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Q: b) Find the derivative of f at the point P( – 3, – 2) in the direction of ü = ( – 1, – 1) fu( – 3, –…

A: The given function is fx,y=-0.02x2y3. Compute the gradient of f as follows. ∇fx,y=∂∂x, ∂∂y…

Q: III. Find the indicated derivative of the following. 2. y +y x , y" 3. (x+ y)2 +(x - y)z = a , y" 4.…

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Q: Q3/ Find the directional derivative of the function f(x,y,z)=xy+yz+zx at the point Po(1,-1,2) in the…

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Q: Find the derivative of the function f(x y) =x2+ xy + y2 at the point (6, 7) in the direction in…

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Q: Find the derivative of the function. f(e) = (3t + 18)2/3 2 f (e) = 3/3t + 18

A: Topic:- derivatives

Q: Find the derivative of the function. f(z) = ez/(z - 9) f'(z) =

A: Explained below...

Q: Find the derivative of the function at Po in the direction of u. x-y g(x,y)= xy+2 Po(1,-1), u=12i+5j…

A: Given :g(x,y)=x-yxy+2u=12i+5j

Q: Find the derivative of the function at P, in the direction of A. 0. fxy,2) 3D ху + yz +zx, Pо(3, -…

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Q: Find the derivative of the function at P0 in the direction of u. f(x, y) = 3x 2 + 4y, P 0(8, 7),…

A: Directional derivative: - The rate at which any function changes at any given location in a fixed…

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

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Q: Find the derivative of the function at the given point in the direction of A. f(x, y) = -10x2 + 5y,…

A: This question is related to directional derivative of a function, we will solve it by finding…

Q: The directional derivative of f(x, y) = In(x² + y²) at the point P(-5, 21) in the direction i = (9,…

A: Given  fx,y=lnx2+y2 To do find the directional derivative of fx,y at the point P-5,21 in the…

Q: Find the derivative of the function. 4 q(y) = 3y? (2y? + 1) q'(y) =

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Q: Q/ Find the derivative of R(z) = → 1 8z4

A: Given function is  Rz=6z3+18z4-1z25Rz=6z32+18z4-1z25Rz=6z-32+z-48-z-25

Q: Find the derivative of the function. z(=) = v + 5 7

A: d/dx (xn ) = n.x(n-1)

Q: Find the derivative of the function y = x²e\" Select one: O a. xe"(3 – 2x) O b. xe"(3 + 2x) O…

A: rule:chain rule of derivativeddxg(x).h(x) = g(x) ddxh(x) +h(x) ddxg(x)

Q: Find the derivative of the function Z=3t^(11/3)-2t^(9/4)-t^(1/2)+1

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Q: Find the derivative of the function at Po in the direction of u. X- y g(x,y) = Po(- 1,1), u= 12i +…

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Q: Find the derivative of the function at P0 in the direction of u. f(x, y, z) = -9x + 3y + 8z, P…

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Q: 5z Find the derivative of the function w = 1+4z dw dz

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Q: Evaluate the directional derivative of the function f =x² - y° + 2z? at the point A (1,2,3) in the…

A: The directional derivative of a function f at a point a in the direction of a vector v is…

Q: Find the derivative of the function. f(t) = 4(t3 − 8)5

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Q: Find the derivative of the function. z = 5t17/5 - 2t9/4 – t1/2 + 8 z' =

A: Use the basic concept of derivative that is power rule of derivative and simplifie.

Q: Calculate the second and the third derivative of y=3x−5/x y^n= y^m=    Calculate the second and…

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Q: Find the derivative of the function

A: We know that,

Q: Use the Chain Rule to find the derivative of the function. y = (x + Sx?)-1

A: Derivative of function

Q: Find the derivative of the function f(x, y) x² + xy +y2 at the point (6, 7) in the direction in…

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Q: find the directions in which the functions increasemost rapidly, and the directions in which they…

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Q: Evaluate the derivative of the function at the given point. 1 y%3D 4t + 9 .t%3D2 (Type an integer or…

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Q: Find the derivative of the function f(x,y) =x² + xy +y at the point (-6, - 5) in the direction in…

A: Given: f(x, y)=x2+xy+y2 To find: The derivative of given function in the direction in which function…

Q: Find the directional derivative of the function at the point P in the direction of the point Q. f(x,…

A: Find the directional derivative of the function at point P9,9 in the direction of the point Q12,5.…

Q: Find the derivative of the given function.   f(z)=−1/z^5.9

A: Write f(z) using exponent.

Q: (x² – y²)² – 4ay³ = yCosx + xCosy = 1

A: We have to find the derivative of the above functions .

Q: The directional derivative of the function function = x - xyz + y? at the point (1, 2, -1) in the…

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Q: Find the derivative of the function. G(z) = (1 – 3z)2V z? + 1 G'(z) =

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Q: Find the derivative of the function. 6. s(t) = 49 (6t - 7) %3D s'(t) =D %3D

A: Use the formula for derivative of a power of a function.

Q: Find the derivative of the function at Po in the direction of A. f(x,y) - - 3ху + 5y, Po(1, - 5), А-…

A: We have to find the directional derivative of the function P at (1,-5).

Q: Find the derivative of the function. h(s) = -2/ 9s² + 2 %3D h'(s) = %3D

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Q: Find the derivative of the function. F(z) = e7/(z – 2) %3D 2e²/(z-2) f'(z) (: – 2)² II

A: f(z)=ezz-2now differentaating both sides with respect to "z"Thenddxf(z)=ddxezz-2…

Q: Find the derivative of the function f(x,y,z) = In (xy + yz + ZX) at the point (8,16,24) in the…

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Q: Find the derivative of the function at the given point in the direction of A. f(x.y,z) = In (x…

A: Solved below.

Q: Find the derivative of the function. f(t) = 7/(root(3, 8t ^ 2 + t))

A: We  Apply the chain rule of differentiation. And formula ddt(f(g(t))= f'(g(t)).g'(t) (this is…

Q: Find the derivative of the function. 7 y = - Choose the correct answer below. OA. (x*) (6x³) –…

A: Use quotient rule of differentiation. Use power rule of differentiation.

Q: Find the derivative of the function. Z = 5t11/5 - 2t7/4 - t/2 + 7

A: Solve for the derivative

Q: Find the derivative of the function. q(y) = 5y (3y +4) q'(y) = %3D

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Q: Find the derivative of the function at Po in the direction of A. f(x.y.z) = xy + yz + zx, (1.-1,-…

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Q: Find the derivative of the function. f(z) = e7/(z – 6) f'(z) :

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Q: Find the derivative of the function f(x, y) = tan-1Y at the point (-6, 6) in the direction in which…

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