d the directional derivative of V = r²z sin o along the direction A = 3r - 22 N evaluate at (1,"/4,2)

Q: A particle moves on a straight line with velocity function v(t) = sin ωt cos2ωt. Find its position…

A:

Q: 5. Determine the equation of the tangent line to (a) r= 2 sin e at = (b) r =1+ cos 0 at 8 =

A:

Q: find the directional derivative of the function at P in the direction of PQ.

A:

Q: In Exercises priate variable. 21. y = cos (r) 23. y = sin-'V21 25. y = sec (2s + 1) find the…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: A particle moves along a straight line with velocity function  v(t) = sin t - cos t and its initial…

A: Given that a particle moves along a straight line with velocity function vt=sint-cost and its…

Q: dy of the function y = sec dx (1+ V4 + sin" (4 + z²). Find the derivative 山心

A:

Q: a.) [ sec²(t − 1) dt b.) 2 √t c.) [ sin(Int)

A:

Q: dy For the function dt = 3 cos t, the third dy order derivative is dt3 -3 sin t -3 cos t 3 cos t 3…

A: Find the third derivative of the first derivative  function

Q: X = r sin cos i, 2 = r cos 0 y = rsint.sinu, Using the given coordinates, find the du directional…

A: Using partial derivatives and chain rule

Q: az Find dz by implicit differentiation, and confirm that the and dy results obtained agree with…

A:

Q: sin(x) sin(y)dx + cos(x) cos(y)dy = 0, y (0) = 2, h = 0.5, Find y (1) using fourth-order RK

A: 4th order RK method  yi+1=yi +16k1+2k2+2k3+k4Where ti+1=tn+h          k1=fti,yi,…

Q: A particle moves in a straight line with the velocity function v(t) = sin(wt)cos*(wt). Find its…

A:

Q: &y dy :5 cos t, the third order derivative dt For the function dt3 is 5 cos t -5 cos t -5 sin t cost

A: Here we will find 3rd order derivative

Q: Find the tangent line to the curve x cos y + y cos x = 1 at (0,1). O A. (cos 1)æ + y = 1 O B. x + y…

A: We can find the tangent line as below

Q: Compute the derivative for r(t) = (cos(8t))i + (sin°(t))j + (tan(6t))k.

A: Derivative of r(t) = cos (8t) i + sin9(t) j + tan (6t) k

Q: A particle moves along a straight line according to the velocity function v(t)=sen(ωt) cos2(ωt).…

A:

Q: Find directional derivative for f(x,y) = y +, Xo = 4, yo = 5, nx = 1, ny = 0. df ðf af -Nx + -Ny=|…

A: We will evaluate the required values.

Q: What is the equation of line tangent to sin r+1 y = at the point (T, -1)? cos E O y= TX –1 - O y = 1…

A:

Q: A particle moves on a straight line with velocity function  v(t) = sin(ωt) cos2(ωt).  Find its…

A: The given velocity function is,

Q: ind the directional derivative of f(x, y) = y² cos(2x) at the point P (, 2) in the direction of u =…

A: fx,y=y2cos2x∇fx,y=-2y2sin2xi^+2ycos2xj^

Q: Find the directional derivative of the function f(x, y, z) = 3e" sin(xy) in the direction of v = 3i…

A:

Q: 12)Find the derivative of y with respect to z. Y= 6^(z^3) Dy/dx =

A:

Q: A particle moves along the x-axis with velocity dx/dt = ƒ(x). Show that the particle’s acceleration…

A:

Q: Find the directional derivative of k(r, y) = 3edr sin(y) at the point (0, ) in the directi

A:

Q: sin(x) sin(y)dx + cos(x) cos(y)dy= 0, y(0) = 2, h = 0.5, Find y (1) using fourth-order RK

A: We have to find y(1) using fourth-order RK.

Q: Q1: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i – 3j…

A: (a) Given S=ln(2x+3y) Differentiate S partially with respect to x and y Sx=22x+3y…

Q: 5. For ø = z sech¬²[y tan¬²(In x)], find the directional derivative when dx = 2dy = -3dz at a point…

A: Given dx=2dy=-3dz⇒dx6=dy3=dz-2 v=6 i+3 j-2 k ϕ=zsech-1ytan-1ln x ∇ϕ=∂∂xi+∂∂yj+∂∂zkzsech-1ytan-1ln x…

Q: dy For the function dt d°y order derivative = 4 cos t, the third is dt3 -4 sin t -4 cos t 4 sin t -4…

A: Differentiate the given function expression with respect to t twice to find the required value

Q: 10x Find the directional derivative of f(x,y) = at P(5,0) in the x + y direction of Q(4, –3). NOTE:…

A: Here is the solution:

Q: a) Find the derivative of f(x,y) = xe* +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j.

A:

Q: nd the derivative of (z.x)= X+c Cos (27 X) Point (0,2,1) in the direction at of V=i-sj+k

A: Directional derivative is dot product of gradient and normalised vector.

Q: The derivative of f(x, y) = e* sin y in the direction of 0 is given by cos y-V3 sin y Du f(x, y) =…

A:

Q: 2(z–1) sinh z cosh I + 3(x – 1)'sech? (z)? Which among the choices will result to a derivative of O…

A:

Q: Find the linear approximation to h(y) = Sin(y+ 1) at y =0 Use the linear approximation to…

A: This is a problem of linear approximation.

Q: Find the rate of change of f with respect to t along the curve. f (x.y,z) =y² - sin(x +z),7(1) =…

A: According to the problem, we have

Q: The third derivative of y = cos 1 sin 27 1 111 a) y" b) y" 27 %3D 3 1 1 c) sin d) y 27 y = - %3D 27…

A:

Q: The derivative of the function y = cos -1 = COS Va at 1 is equal to 4 :Select one -2 .a V3 .b V3 .C…

A:

Q: Find the point of intersection of the tangent line to v=sin(2r) at y=0 and the line %3D x+2y=5.

A:

Q: 5. For ø = z sech¯³[y tan¬²(In x)], find the directional derivative when dx = 2dy = –3dz at a point…

A: Given function is ϕ=zsech-1ytan-1lnx we have to find the direction derivative of given function when…

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 ex cos (yz),…

A:

Q: Find the directional derivative of the function in the direction of u = cos(e)i + sin(@)j. F(x, y)…

A: Explained below

Q: Q /Choose the appropriate derivative for this function y = (x+ 1)2* dy = 2* (x + 1)2" - In(x + 1) dx…

A: Explanation of the answer is as follows

Q: Find the equation of the tangent line to the graph of F(r)= 2z²+2r+1 evi dy at r 0. sech z

A:

Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 7 tan-1 ; P(-8,8); а%3…

A:

Q: Compute the derivative for r(t) = (cos(8t))i + (sin°(t))j + (tan(6t))k. %3D dr dt

A: Given

Q: Q1: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i…

A:

Q: (a) If f(x.y) = e siny - e sinx then verify that fry fyz- %3D

A:

Q: A particle moves in a straight line with the velocity function v(t) = sin(wt)cos°(wt) . Find its…

A:

Q: Find the directional derivative of f(1, y) = Ie – ye² at (0,0) in the direction of w = 5i – 25.

A: