Consider the following equation f (x,y) = x²y. Find the derivative off in the direction of (1, 2) at the point (3, 2) is %3D A 30 V5 В. 30

Q: Get the derivative of dz/dx. XY z =

A: Here we will find the derivative dz/dx,

Q: Find the directional derivative of z = f (x, y) = x²y³ – 3y² at (-3,4) in the direction of the…

A: Use directional derivative formula which is mentioned in solution.

Q: Find the derivative of y with respect to x, dy/dx of X=y^3/3+y

A: The given equation is x = y3/3 + y Differentiate on both side with respect to x d/dx(x) = d/dx (…

Q: Find the derivative of the function f (x, y) = x²y + y²z: at Po(1,2,3) in the direction of û = 2î –…

A: To find the derivative of the function f(x,y)=x2y+y2z at P0(1,2,3) in the direction of…

Q: Find the derivative of y with respect to t. 10t y3Dcsc dy %3D dt

A:

Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

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Q: Calculate the derivative of y with respect to x. xe' = 3xy + 5y dy dx

A: We have to find

Q: Use the chain rule to find the derivative of w= x + y with dw with x cost + sint, y= cost– sint dt…

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Q: Find the derivative of y with respect to t. y= sin 1(10t) dy dt %3D

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Q: Find the derivative of y with respect to s. y%3Dsec -1 (2s4 + 7) dy ds

A:

Q: 1. Use the definitio

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Find the derivative of y with respect to t. y = t(In 11t)? dy %3D dt

A:

Q: Find the derivative of y with respect to x. y = In (x) dy 8. dx %3D

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Q: Find the derivative of the function y = 5 . 5t +3·3. dy dt

A:

Q: Why does this work? If we have the curve in the xy-plane: F (x, y) = 0, then why is the implicit…

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Q: If f(x,y) = ln(xy) + x2y2, in what directions is the second directional derivative of f(1,1) = 3?

A: Given function fx,y=lnxy+x2y2 Consider unit vector u⏞=12,32  Now, Du⏞f=∇f·u⏞             ∇f=fx,fy…

Q: The directional derivative of f(x, y) = 2e* cos y at (0, ) in the direction of v = (-6, 8) is

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Q: Let f(x, y) = V xy. Find the derivative of f. af 1 ду 2

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Q: In what direction is the derivative of ƒ(x, y) = xy + y2 at P(3, 2) equal to zero?

A: Consider the function and solve.

Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2xy - 3y2, P0(5, 5), v =…

A: The given function is ƒ(x, y) = 2xy - 3y2. Note that fx=2y    and  fy=2x-6y. at P0=5,5,  fx=10   and…

Q: (a) Find the derivative of ƒ(x, y, z) = x3 - xy2 - z at P0(1, 1, 0) in the direction of v = 2i - 3j…

A: We have given function fx,y,z=x3-xy2-z, point P01,1,0 and vector v=2i^-3j^+6k^

Q: Find the derivative of the function. s=t° In t| ds dt

A: The solution is given below in the next step:

Q: Find the particular anti derivative that satisfies the following conditions:  dy/dx = 7x^-2 + 5x^-1…

A: dydx=7x-2+5x-1-5dydx=7x-2+5x-1-5dy =( 7x-2+5x-1-5 ) dx

Q: In what direction is the derivative of ​f(x,y)=xy+y^2 at ​P(5​,4) equal to​ zero?

A: Given,

Q: Calculate the derivative of y with respect to x. xe' = 3xy+6y %3D dy dx

A:

Q: : Find the derivative of f(y, z) = ze2y + cos(2zy) at ppoint (9,1,0)in the direction of V = 2i – 3j…

A: This is directional derivative, just write the formula and solve accordingly.

Q: Find the derivative of the function. -1 y = (3t – 1)(6t – 5) dy dt II

A:

Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

Q: In what directions is the derivative of f(x,y) = xy + y at P(4,5) equal to zero?

A:

Q: Find the derivative of y with respect to x. y = (3x + 4)* dy %3D dx II

A:

Q: Calculate the derivative indicated.

A: Since, y=4t-3+3t2  -(i)dydt=ddt4t-3+3t2=-12t-4+6t⇒dydt=-12t-4+6t

Q: Find the derivative of f(x, y) = xe + cos(xy) at the point (2,0) in the direction of v=3i-4j. B) 5 O…

A: Please find the answer in next step

Q: Find the derivative of y with respect to t. 1 y = sec 1 0<t< 5t4 dy dt

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Q: Find the derivative of y with respect to z. y=5(2%) dy dz

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Q: Calculate the derivative indicated.

A: We have to calculate the indicated derivative drdtt=4 for the given function: r=t-et We know the…

Q: What is the derivative of h(x, y) = e"Y at (2, 3) in the direction at an angle of 7 from the…

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Q: Find the derivative of y with respect to s. y = sec 1 (5s° + 2) dy ds

A:

Q: Find the particular anti derivative that satisfies the following conditions: dy/dx=3x+5/sqrt3 of x;…

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Q: In what direction is the derivative of f(x,y) = xy + y at P (3, 2) equal to zero?

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Q: Find the derivative of y with respect to z. y=3 (2°) dy dz II

A: We have to find the derivative of y with respect to z when y=3z9 Taking log both sides,…

Q: find the derivative of the function at P0 in the direction of u. ƒ(x, y) = 2xy - 3y2, P0(5, 5), u =…

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Q: dw B) Use the chain rule to find the derivative dt of w = x2 + y2 with x cost, y = sint.

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Q: Find the derivative of f(x, y) = (2x – y°, sin(ry), r²y*)

A: Given f(x,y)=2x-y3,sin(xy),x2y3 differentiate f(x , y) with respect to x we get…

Q: In what directions is the derivative of f(x,y) = xy + y at P(8,5) equal to zero?

A:

Q: Find the derivative of y with respect to v. y=v/1-v +5 cos 1v V dy dv II

A:

Q: Find the derivative of the function. y = (3t – 1)(6t – 6) -1 dy dt II

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Q: Compute the second derivative of e^x+y+y^2+x^3=0. y" denotes, d^2y/dx^2

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Q: Find the particular anti derivative that Satisfies the following conditions dy 4x +3 ; y(1) = 8 dx…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.