Q1J Use the Chain rule to find the derivative of w=xy + In z with re spect to v if x v/u, y u+v, z cos u.

Q: Compute the derivative of f(t) = (3t2 + sin t, cos3 t + 8t2, 5tan t) relative to t.

A: d(u+v)/dt=  du/dt + dv/dt

Q: If z = (x +y) eª and ¤ 3t and y = 1 – ť², find the following derivative using the chain rule. Enter…

A: See the attachment

Q: Evaluate the derivative of z f8.png asin (bvx3) f(x): %3D c2x + In(kx) if a = 15.08, b = 5, c = 5,…

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Q: Find the derivative of y with respect to the independent variable. y = 9cos zO O A. - 19cos AO In 9…

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Q: 4. Use the chain rule to find out the total derivative dv/dt, when v = xe/z, where r = t²,y = cos t,…

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Q: Use the Chain Rule to find the derivative of w = xy with respect to t along the path x = cos t, y =…

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Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: Given:        x2+2xy=y3

Q: find the derivative of the function at P0 in the direction of u. ƒ(x, y) = 2x2 + y2, P0(-1, 1), u =…

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Q: If z=(x+y)e^y and x=7t and y=1−t^2, find the following derivative using the chain rule. Enter your…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

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Q: Find all second order derivatives for z= 9y e TX. %3D

A: Solution of question as follow

Q: 12. Find derivative of the following composite function using the Chain Rule: 2y t(y) = 6y² + 1+y?…

A: We have to find derivative

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: Find the derivative of the function. rsin(x) In(2 + 9v) dv Jcos(x) y'(x) =

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Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1,1) in the direction of from the…

A: We have to find the directional derivative.

Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: Use the Quotient Rule to compute the following: t2 +1 d at t = 2 dt t2 The derivative is:

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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: Use the Fundamental Theorem of Calculus to find the derivative of Cos t -dt t11 -3 dy dx II

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Q: Let f(x, y,z) = z-sin(xy), x t, y Int, z et1. Find derivative of f directly and by using chain rule…

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Q: let f(x,y)= z-sin(xy),x= t, y= lnt, z=e^t-1. find derivative of f directly and by using chain rule…

A: Plug the given expressions of x,y, and z. Then differentiate directly. And plug t=1

Q: Find the derivative, dy/dx: In-2x O y = -() In' 1-4 la > 是 In' x 2/1+2In ४ In' z In z 2w In² z ) In'…

A: This question is based on diffrentiation.

Q: Find the derivative of the function. r sin(x) y = Jcos(x) In(4 + 9v) dv y'(x) = %3D

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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 y with respect to x, t, or 0, as appropriate. 1-x y = In (x + 2)5 4x - 7 (x +…

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Q: Q2 find the derivative of the following: 1) y = 2sin?(5x) ,2) y = lnx'ncosh 5x ,3) xsin-14y = y…

A: See the attachment

Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: Suppose that x and y are both differentiable functions of t and are related by the given equation…

Q: H.W: Use the chain rule to find the derivative === with x = cos² t, y = sin² t, z = - at t = 3 dw xy…

A: Solution :

Q: Find dw/ds and dw/dt using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x-s+t, y =…

A: The given function,w=sin(4x+5y)x=s+ty=s-tat the point s=0, t=π2

Q: 2. Show that the function psin(2r) e-*dt g(x) = is differentiable on R and compute its derivative.

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Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = x2 + 2y2 – 3z?, Po(1,…

A: We can solve this as follows:

Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 6x+10y,…

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Q: 4. Show in two ways that the function f(z) = exp(z²2) is entire. What is its derivative? Ans. f'(z)…

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Q: In the integration What is the implicit derivative of u? V9-4x* a. du = 2dx b. du = * c. du =– 2dx…

A: Implicit differentiation of integral

Q: If z=(x+y)e^y and x=7t and y=1−t^2, find the following derivative using the chain rule. Enter your…

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Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

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Q: Find the derivative of the function. a. y = In(x + Vr² – 1) b. f(x) = log2 (e "cos Tr) COS

A: According to our policy, when multiple questions are posted we solve only the first question. sorry…

Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

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Q: Find the derivative of y with re Ind the (x* In x) y = dy dx II

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Q: Find Zxx=Zyy=Zxy=

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Q: 3. Find the derivative of f(x, y, z) = z2 + ye" at (In 2, 2, 1/2) in the direction in which the…

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Q: Find the derivative of y with respect to x in the f a) y = u u +1 and u= 3x - 2 b) y=Vu + 2u and u=…

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Q: Evaluate the 3rd derivative of M with respect to (x) M= x6 y3 Cos (x6 y3) if x =6 and y= 3

A: The function is M=x6y3cosx6y3. Using implicit differentiation, find dydx.…

Q: Calculate the second-order partial derivative of f(x.v) =sin(x³v?) with respect to x and y, that is,…

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Q: 3r %3D 5r + 2 – 1 (d) f(x) =

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Q: Find the derivative of g(x) = |. •r In z Vt2 +t+1 dt

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Q: Let f(x, y,z) = z-sin(xy), x = t, y = In t, z = e4. Find derivative of f directly and by using chain…

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Q: Find the derivative of y with respect to x. y = tan -1V3x O A. V1- 3x 1 O B. 2(1 + 3x)/3x 3 Oc.…

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Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))