Find r(t) for the given conditions. r'(t) = 8e4ti + 9eʻj, r(0) = 2i r(t) =

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Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = 4e* + 4x²; F(0) = -5

A: Given query is to solve the differential equation.

Q: dw Use an appropriate form of the chain rule to find dt = In(10x² – 2y + l2³); x = tỉ, y = tỉ, z =t?…

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Q: (B) The point on the curve r(t)=Dti + (1 + r)j at which r(t) and r'(t) are perpendicular is (1,0).

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Q: Find the differential df of the function f given the gradient. Vf = (5x + 6e" ) i + 6xe' j. df =

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Q: Use the Chain Rule to find dw/dt. + y2 + z2 x = 5 sin(t), y = 7 cos(t), z = 6 tan(t) W = In

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Q: Find the general solution for y(t) where, dy 10t dt y II

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Q: B. If R = xyz’i+÷j – yz*k_find of the differential R, dR.

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Q: . We are given r'y-5x+24y 6/ỹ, where x and y are both functions of t. If dx = 2, x= 1, and y=9, what…

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Q: Use the chain rule to express dy /dx in terms of x and y y = sin t and t = cos x where t=0

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Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: Find the differential dy of the given function. (Use "dx" for d> y = 8x² – 4 dy = %3D

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Q: Find the differential dy. (a) y = xV10 - x dy = -2 (b) y = (1+x) ? dy =

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Q: The general solution dx/dt t+x of t > where t > 0, is x(t) =

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Q: . The exact differential d(xy)= xdy + ydx, what is the d( = 4x²y'dy+2xy*dx.

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Q: hello! can you help me with this calculus problem?

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Q: d use the Chain Rule to calculate f(r(t)). dt f(x, y) = x² – 3xy, r(t)= (cos t, sin t), 1 = }

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Q: Use the Chain Rule to find dw/dt. In(Vx² + y² + z² ), x = 3 sin(t), y = 5 cos(t), z = 6 tan(t) W =…

A: We have to find the derivative  using chain rule.

Q: at (s, t) = (0, 1) if ds z = 6x + y² tan (), x = e" – st, y = s² – f.

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Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using…

A: The given function is w=8x2+3y2, x=cost and y=sint. We have to express dwdt as a function of t.…

Q: Find the differential dy and evaluate dy for the given values of x and d.x y = Vx2 + 24, x = 1, dx =…

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Q: Find the differential of the function. y = V6 - t8 dy %3D

A: Solution: The objective is to find the derivative of the given function

Q: dz Use an appropriate form of the chain rule to find dt z = 7 cos x – sin xy; x = ;, 1 y = 9t Enter…

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Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

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Q: Without eliminating the parameter, find d²y at t = 2 1 x = 1

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Q: dz Use an appropriate form of the chain rule to find dt z = 4x°y³; x = tº, y = t" Enter the answer…

A: From the given problem: z=4x6y3 ; x=t8 , y=t7 Now apply the chain rule.…

Q: Find the differential dy of the given function. y = V9 - x dy

A: Given y= √(9-x2) To find dy/dx

Q: Let z(x, y) 2x2 – 3y? where a 2s – 4t & y = 9s + 8t. he at dy dx az Calculate ds dz by first finding…

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Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

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Q: Find the general solution of this DE using INSPECTION. dnda + +(x? t y?)dx = 0 2 aycdly

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 9x2 – - 6 dy = f(x)dx

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Q: Given z = 3x'y + V5 cos 2y-2x, detemine the total differential o

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Q: The linear approximation at and where B is: = = 0 to sin(9x) is A + Bx where A is:

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Q: Use the Chain Rule to find dz/dt. z = sin(x) cos(y),    x = The Square Root of t,    y = 8/t

A: Given: z = sin(x) cos(y),    x = √t,    y = 8/t By Chain Rule,

Q: Find the total differential. w = e7Y cos(4x) + z7 dw

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Q: Find the differential df of the function f given the gradient. Vf = (4x + 6e) i+ 6xe"j. df =

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Q: the given velocity v(t) = e2ti– sin tk and r(0) = (1,2,0) to find the position at time t = 1.

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