In Exercises 1-6, use the Product Rule to calculate the derivative. dh h(s) = (s¬1/2 + 2s)(7 – s=1) %3D ds s=4

Q: Q4/(A) Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction.

A: The given function is fx,y=xey+cosxy at the point 2,0. Find the derivative of the function. Here we…

Q: Calculate the derivative of the function xe" at the point x = 0 %3D O 1 e O 2e

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Q: dx y=u(1+u°)³ and u =(3x-2)². %3D Express the derivative in terms of x, if

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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: 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: (d) Find the directional derivative of f(x, y) = x²e¬y at (-2,0) in the direction towards the point…

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Q: Compute the derivative of f(x) = (sin x)v , 0 < x < T.

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Q: III-Déterminer la dérivée de : a) f(x) = lnx lnx + 1 III- Determine the derivative of: ex +1 J b)…

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Q: Find the derivative of the function. 2x F(x) = arctan(t) dt Vx F'(x) : %D

A: The given problem is to find the derivative of the given definite integral function. We have to use…

Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: Find the derivative of the function. %3D y = log |3- 5x| dy

A: Here , we will differentiate y  with respect to X  .

Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

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Q: Find the derivative of the function at Po in the direction of A g(x, y) = x - (y/x) + V3 sec (2ry),…

A: Let us consider the given function z=f(x,y) The directional derivative of the function at Point P in…

Q: Find the derivative of the function at Po in the direction of A. f(x,y) = - 4xy + 3y², Po(4, - 2),…

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

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

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Q: Find the derivative of the function at P, in the direction of A g(x,v) = x - (y² /x)+ V3 sec (2xy),…

A: Given that  g(x,y)=x-y^2/x+√3arcsec(2xy) P(1,1) and A=12i+5j To find the directional derivative of g

Q: Find the derivative of f (x y z) = x^3 − xy^2 − z at (1, 1, 0) P0 in the direction of A = 2i - 3j +…

A: Given,           f(xyz)=x3−xy2−z  and point Po =(1,1,0) and the direction vector A=2i-3j+6k.

Q: y=In(x dy -

A: Given : y = ln1xx-5

Q: In Exercises -. , find the derivative of y with respect to the appro- priate variable. 37. y = sV1 –…

A: Since, you have asked multiple questions we will answer the first one for you. If you want any…

Q: Find the derivative of the function at Po in the direction of u. 3x f(x, y) = tan -1 , P0(-2, 3), u…

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Q: Find the derivative of the function f(z,k) = z^4— 16k^3+ tanh(z) — 4 csc(k) in terms of z and k ?

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Q: Find the derivative of the (e) h(x) = e5 sin (Væ) + a° sec ()-

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

Q: What is the derivative of y e3a + 1 3e3 %3D (e + 1) 3e3z (e + 1) O y = 12e6 +3e3 %3D (ed + 1) O y =…

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Q: Calculate the derivative d da 34 dt using Part 2 of the Fundamental Theorem of Calculus. 34 d dx…

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Q: Using the definition, find the derivative of fz) = 3 z^-6 z² at point z= 0

A: Given,          fz=3z4-6z2

Q: et y = (xº + 4)*. + 4)*. se the General Power Rule to find the derivative.

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Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. Зх + 7 y…

A: Derivative of the function using fundamental theorem of calculus is

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: What is the first-order derivative of y = x^y?

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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: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: Calculate the derivative d dx t14 + 5dt using Part 2 of the Fundamental Theorem of Calculus.

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Q: %3D 10. Find the derivative of the function )= V 5T4 using the limiting process.

A: Given,

Q: Find the derivative of the function In t dt.

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Q: 3r %3D 5r + 2 – 1 (d) f(x) =

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Q: 1. F(x) = S, t³ - 5t dt

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Q: Determine the derivative of the function (x) = %3D 3+e3*

A: Authoring guidelines:…

Q: Find the derivative, or y', of ³ – Vy = ¿y² + 6 at (2,1).

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Q: -2 In(x) Consider the function f(x, y) = 3y

A: We have to find the derivative of the function f(x,y) in the direction u=-5,2.…

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: In Exercises 7–12, use the Quotient Rule to calculate the derivative.

A: gt=t2+1t2-1 We need to find the derivative of the function at t=-2

Q: Find the derivative of the given function a. F(x) = dt 1+ b. g(x) = [ - dt sinx 1+1*

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Q: Find the derivative of f(x, y) = e- x ln(y² + 1) at the point R(4,0) in the direction of w = (2, 1).

A: NOTE: Refresh your page if you can't see any equations. . the given vector is find the unit vector