A. Find the derivative of the function at o P in the direction of A f(x, у) — х — V3sec-1(2xy)at P,(1,1) and A %3D X 12i + 5j

Q: Find the derivative of the function at P0 in the direction of u. f(x, y) = ln(-9x - 4y), P 0(4,…

A: use gradient for finding the directional derivative.

Q: Find the derivative of y with respect to x. y = tan (In 3x) O A. 1+(In 3x) 21 O B. x(1 + ( In 3x)) 1…

A: Given: The function y=tan-1ln3x, To determine: The derivative of y with respect to x,

Q: Find the derivative of the functions. a. y= e5x b. y= er-3 c. y= ecos x d. y= e2 sin x e. y= e* sin…

A: We need to find the derivative of the functions. First we should know the following differentiation…

Q: Find the equation of the tangent line at y = 0, given the inverse function x = (3y + 2)V + 1)². A) y…

A: Given equation is x=3y+2y+12. We have to find the equation of the tangent line at y=0. At y=0, x=2…

Q: Find the derivatives of y with respect to x: a) y = xe* - e* b)' y = e(4x+) e(tx+) X. c) y = e*(sin…

A: Since you have posted multipart question and we can answer three subparts. So, answered first three…

Q: Find the derivative of f (x) =/ csc(etr+1) . 2e 4r +1 A Vese(eti +1) 4x - 2e r +lcsc2(e4x+1) B…

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Q: Q2) Find the derivative of the function at Po in the direction of A. g(x, y) = x – (y/x) + V3 sec…

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

Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: Find the derivatives of y with respect to x: a) y = xe* – ex b)' y = e(+x+) c) y = e*(sin x + cos x)…

A: Differentiate the function with respect to x.

Q: Find the equation of the tangent line at y = 0, given the inverse function x = (3y + 2)(y + 1)2. O y…

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Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: Find the derivatives of the following functions: (a) y = Jx² +sec(2x+3) Co bno %3D (b) y =…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: The total derivative of the function ƒ(x,y) =x²y at x = 1,y = 2 and dx = - dy = 2 is O a. 20 O b. 21…

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Q: Find the equation of the tangent line at y = 0, given the inverse function x = (3y + 2)(y + 1)?. A)…

A: Let's find.

Q: 11. Find the first derivative of y = arccot (). a. y' 1+ b. y' = 1+x² 21 c y' = 14 d. y' = 14x0 e.…

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Q: H.W: 1. find the derivative of the function f(x, y, z) = xy+ yz+ zx ,at the point P,(1,-1,2) in the…

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Q: Find the derivative (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: Find the derivative of the function f(x, y) 5x2-3y at (8,4) in the direction of A = 3 i-4j O 412 492…

A: First of all we will find gradient, then we will find the directional derivative

Q: 2. In each case, find the derivative d (a) z = x* + y and r(t) = In (t) and y(t) = e24, (b) z = 5xy…

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Q: 1. Find the derivative of each given function with respect to x. (i) F(x) = | t dt 1+ t2' (ii) G(x)…

A: FUNDAMENTAL THEOREM CALCULUS If f(x) is continuous over the interval [a,b] and the function F(x) is…

Q: Find the following derivatives. where z= e 9x + 4y x = 3st, and y = 2s + 4t Zs and Zt,

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Q: Q2: Find the derivative of f(z,x) = xe* + cos(2zx?) at a point (0,2,1)in the direction of V = i - 3j…

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Q: Find the vertical trace of the function at x = 1: g(x, y) = cos√x² + y²

A: Definition : Consider a function z=f(x,y) with domain D⊆R2. A vertical trace of the function can be…

Q: Find the derivatives of y with respect to x: a) y = xex – e* b)' y = e(4x+) c) y = e*(sin x + cos x)…

A: Hello, Thank you for the question. Since we only answer up to 3 sub-parts, we’ll answer the first 3.…

Q: Q4: Find the derivative of the function at Po in the direction of A 1) f(x, y) = 2.xy -3y, P.(5,5).…

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Q: Q1 / Find dy/dx by using the definition of derivatives for the following functions; -4 1. у %3D 2. f…

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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.

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Q: H.W: 1. find the derivative of the function f(x, y, z)= xy + yz + zx ,at the point P(1,-1,2) in the…

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Q: Find the derivative of the function using the definition of derivative. dy Ay lim dx A-0 Ar 1. y=37…

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Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: Find the derivative of y = x°e*. O a. y' = 3e*x2(e*+x) O b. y 3x2(e* +1) O c. y = e*x2(x+ 3) O d. y'…

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Q: Q2) Find the derivative of the function at Po in the direction of A. g(x, y) = x - (y²/x) + V3 sec…

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Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x V3sec-1(2xy)at P.…

A: To find the derivative of given function means we have to find the directional derivative of the…

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: 51. grad f = (2x + 3e")7 +3xe'j

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Q: The third order derivative of the function y = In(1 – x) - at x = 0 is et O A. Undefined OB. C. 4 D.…

A: As per our guideline we supposed to answer only first question , kindly re post other as next…

Q: 13. Find the derivative of the function T(z) = dz +b cz +d numbers such that ad – bc + 0. When is…

A: Hello. Since your question has multiple parts, we will solve first question that means question (13)…

Q: Find an equation for the tangent line to the graph of f(x) = -2x2 + 2x + 3 at the point where x = 1…

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Q: Find the directional derivative of the function f(x,y) = 3-6xy+ 10y at the 1 point P (1,5) in the…

A: The given function is fx,y=3x-6xy+10y . Obtain ∇fx,y as follows.…

Q: Assuming that y is defined implicitly by the equation a2 – y² = 61, the derivative dy at - dx (2,…

A:

Q: Let y= 8 x2 - 7. dy = AxB + C. dx Find A, B, and C so that %3D A = B = C = Then find the value of…

A: Given  y = 8x2-7   ......... (1) We have to find the value of A, B, and C such that dydx=AxB+C…

Q: 4. a) Find the following derivatives using differentiation rules. d dx 5 2)* d ii) Vx + dx d²y b) If…

A: 4 First we will see differentiation rules.…

Q: Find the derivatives of each of these functions. a. y = (x¹+csc(z)) ³ b. y=sin(z) sec(41) c. y = csc…

A: Note - As per our guidelines we have to answer first three sub parts if multiple subparts are posted…

Q: Given the curve y2º = x in the xy-plane, for what value of y, if any, does the derivative of y with…

A: Differentiation w.r.t to x

Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x – E) V3sec-1(2xy)at…

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Q: Find the directional derivative of Du f(2,1) in the direction of: d = 7i + 2j To f(x, y) = In(Ges…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: find the directions in which the functions increase and decrease most rapidly at P0 . Then find the…

A: Consider ƒ(x, y) = x2y + e^xy sin y, P0(1, 0)

Q: Find the equation of the tangent Ine at y= 0, given the inverse function x= (3y+ 2)(y+ 1) O y= 7x +2…

A: The solution are next step

Q: Find the derivatives of y with respect to x: a) y = xe* - e* b) y = e(1x+) %D c) y = e*(sin x + cos…

A: (a) The product rule of differentiation is as follows: uv'=u'v+v'u The required differentiation…