d a. (un) b. c. :(7v – 2u)

Q: Find partial derivative, zg and Zy for the following function: e 2x²+3y Z =

A:

Q: Find the partial derivative fx and fy of the given function 3x f(x, y) = -y2 :/ cos(r? – - t + 1)dt.

A:

Q: If f(x, y) = x3 + yt, what is the partial derivative of f with respect to x? A 3x2 B 4y3 3x²+ 4y3

A: Given fx,y=x3+y4

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: z = x3 – xy? + 3y2

A: Let us consider the two variable function z=f(x,y) The first partial derivative of the function is…

Q: Find the four second partial derivatives of the following function. f(x,y) = ln (3x2 + 4y2 + 7)…

A: We have to find

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: If f(x, y) = y² cos(x) – a° In(y), find the second partial derivative

A: Partial derivative problem

Q: If f(x, y, z) 2x5 + 3y5 — 8x2у?z?, - what is the partial derivative of f with respect to z? .A f z =…

A: Partial differentiation of  F(x,y,z) = 2x⁵ +3y⁵ - 8x²y²z² with respect to z

Q: In what directions is the derivative of ƒ(x, y) = (x2 - y2 )/ (x2 + y2 ) at P(1, 1) equal to zero?

A: Given, , the unit vector is , here directional derivative is given as,

Q: If f(x, y, z) 2x5 + 3y5 - 8x2y2z2, what is the partial derivative of f with respect to z?

A: The given function is fx, y, z=2x5+3y5-8x2y2z2.

Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: z = x3 – xy? + 3y² |

A:

Q: Ift=2cos (y² + 2), find the derivative of t with respect to y. A. 8y sin(y² + 2) cos(y² + 2) B. –8y…

A: The given function,  t=2cos2y2+2

Q: find the derivative of y with respect to x, t, or u,as appropriate.17. y = ln (u + 1) - eu…

A: Given, y=ln(u+1)-euDifferentiating both sides w.r.t u we…

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

A:

Q: If s = f(t) denotes the position of a particle at time t, the derivative f'(c) is the of the…

A: Solution:Given      If s=f(t) denotes the position of a particle at time t, the derivative f'(c) is…

Q: Suppose that y is a differentiable function of x andz = cos (x4y9).Express  dz dx  in terms…

A: Given a differentiable function

Q: 2. IShow, using the definition of the derivative, that the function f(x, y) differentiable at every…

A:

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x (x+ 3)5 15) у - In 6х- 8 A)…

A: Given that:y=ln1-xx+35To find derivative

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

A:

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 – 7x³ + 21x² - i) y = (x² +…

A: As per guideline we have to solve first three subparts

Q: Find the Partial derivative of f with respect to y for * 2. y² f (x, y) = x + y

A:

Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d.…

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

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: Find all second-order partial derivatives for the following. f (x, y) = 2y ln x

A: To find all the second order derivative for the function f(x, y)=2ylnx

Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: Find the first partial derivatives of the given functions. z = x3 - xy? + 3y?

A:

Q: Find the Partial Derivatives of the functions with respect to each variable 4) f(x,y)=\x² + y?

A: We have  f(x,y)=x2+y2 So we can write f(x,y)=(x2+y2)12 And we know that ∂(xn)∂x=nxn-1

Q: If z = (x + y) ev and x = 5t and y = 1 – t², find the following derivative using the chain rule.…

A: We are given that z=(x+y)ey,  x=5t, and y=1-t2. Now, we need to find dzdt.

Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

A:

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

A:

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…

A:

Q: The derivative of y with respect to a given ¹ = 1 is Oy' = yx²-¹ O y'= 0 Onone of the choices Oy' =…

A: I have stated the used formula in the solution.

Q: 2) Let f(x, y) = x sin(2y) + 5y¹. Find fyyyyyyyyyy (x, y) (10 partial derivatives), explaining how…

A: Here the given function is f(x,y)=xsin(2y)+5y4x. We have to find the 10 times partial derivative of…

Q: Calculate the derivatives of the following functions.(a) y= 4x2 + 4(b) y = sin 3x+ 4 cos 2x(c) y =3x…

A: We have to find derivative of the given function. (a). dydx=d4x2+4dx=8x   b.…

Q: Find the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.

A:

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

A:

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=…

A:

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz,at the point in the direction of A =…

A:

Q: Find the first partial derivatives of the given functions. 1. z = x3 – xy? + 3y?

A: SOLUTION-

Q: Find the partial derivative of the function with respect to each of the variables f(x.y) =…

A: Given function is fx,y=100x0.64y0.36 find the partial derivative of the function with respect to…

Q: ind the derivative of y with respect to x. y =-cos-16x + 7° 6 6. 1 + (6x + 7)2 81 - (6x + 7)2 O 4.…

A:

Q: Find the third order derivative of y = In(cos(2x))5. %3D A. y' = -40sec² (2x)tan(2x) %3D В. у' 3…

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Q: Letv = x2sin(v) + vexy, where X = s + 2t and y = st-

A: Solution is below.

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))

Q: (1) Suppose that y is a function of r satisfying the equation 5x + 10y + 3.ry+ 5y + 6x 0. Use the…

A: