1. Find the derivative of the function at P in the direction of u. Sketch the graph of each, if possible. a) g(x,y)=*-y xy +2' X-y, P(1,-1), u= 12i + 5j

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 y with respect to x, t, orθ, as appropriate.

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Q: 1.x3 = at?, find the second derivative of "x" with ,d²x respect to "t", 'dt2

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Q: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

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Q: A) find the derivatives for the following: 1) y = In(In(sin¯'(e?r))) – 5-Inx 2) Y=sech-1(log, 93*) +…

A: Chain rule for differentiation: Let y=fghx then dydx=ddxfghx=dfghxdghx×dghxdhx×dhxdx Equation of…

Q: 1. Find the derivative of the following using implicit differentiation. TYON b. BARZ c. y = sec(x +…

A: Since we only answer up to 3 subparts, we'll answer the first 3. Please resubmit the question and…

Q: 1. Find the first derivative of the given function given. a. y = sint cos t b. y = 6 tan(2n + 3x)

A: In this question we have to find the first derivate of the given function.

Q: 11.Determine the equation of the curve whose tangent line at any point (xy) is e* – sin x and passes…

A: Given problem:- Determine the equation of the curve whose tangent line at any point (x,y) is ex -sin…

Q: 7. Compute the derivative of y = tan-(Kr) 1. at the point r = K

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

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Q: Find the derivative of the function at Po in the direction of A. 1- f(x, y) = 2xy - 3y² , Po ( 5,5),…

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

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Q: Find the derivative of y with respect to x. y= sin -3 O A. XV1-x - 3 O B. 1+x - 3x 3 c. 1-x -3 O D.…

A: Given that: y=sin-11x3

Q: find the derivative of y with respect to x, t, or u,as appropriate.55. y = ln (cos^2 u) 56. y = ln…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: sin 0 cos 0 1+ 2 In e y = In

A: Consider the function:y=lnsin θ cos θ1+2 ln θ   =lnsin 2θ21+2 ln θ…

Q: Find the derivative of y with respect to 0. y = In (4 cos20) dy de

A: Given, y = ln4cos2θ  We have to find dydθ

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: /4 Find the derivative of y with respect to t. (a) y = In(3te-1) (b) y = esin t (In t² + 1) (c) y =…

A: Given functions,  (a)  y=ln3te-1 (b)  y=esintlnt2+1 (c)  y=tlog3e(sint)(ln3) The objective is to…

Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

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Q: find the derivative of y with respect to x, t, or u,as appropriate. y = e^(cos t + ln t)           .…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

Q: Find the derivative of y with respect to z. y In (sinh 3z) y -

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Q: Find the derivative with respect to x. (c) y = v7x – x4 (d) y = (1+ sin 7.x)-5 (a) y = (5x – 2)*…

A: This question is related to derivative, we will solve it using given information.

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: 1. Find the first derivative of y with respect to x (y') of the given functi 1. x³y-xy² +x² +y? = 0…

A: To find the first derivative of y using the given equation.

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

A: Given problem:-

Q: Find the derivative of y with respect to t at t=2 if a) y = cos (x) – cos(1+x²) and x = [sin(t – 2)…

A: The derivative of y with respect to t is:

Q: 1) Find the Linearization x of the function -V1+2x when x is near 0 Find the equation of the tangent…

A: As per Bartleby guideline if more than one question is asked only first question to be answered…

Q: 6. Let y + xy - y = 8x*. a) Find dy/dx using implicit differentiation. b) Find the equation of the…

A: In implicit differentiation, when we differentiate y, we use dy/dx

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

A: we have to find directional derivative.

Q: Can you help me step by step?

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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: 1. Find the first order derivative of u = x*.

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Q: Can you help me with this problem step by step?

A: Given:

Q: -7/2 = 8. Calculate the derivative of y with respect to , if x/2 + y dy dx

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Q: 2. : Consider the function ry + cos y + x 2+ xy. (a) Find the derivative, dy/dx. (b) Find the…

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Q: Find the partial derivative of the function with respect to each variable. h(p,p,0) = p cos p sin 0…

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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.…

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Q: Q1: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i…

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Q: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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Q: 14. Consider the curve defined by x2y2 - 3x2 - 6y2 0. dy a. Use implicit differentiation to find :…

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Q: 3.9.27 Find the derivative of y with respect to x. y = sec 1(5x2 + 1). -1(5x2 +1), x > 0 dy %3D dx…

A: Please see the answer in Step 2

Q: Find the derivative of the function at Po in the direction of A. f(x,y)=-3xy + 5y², P₁(-10,2),…

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Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: Find the derivative of y with respect to x: ,2 2 X'e y = log,2 x+2) Evaluate the integral: -1 cos…

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Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…

Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

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Q: A-The derivative is y = In Vsin 0 cos 0 1 + 2 ln 0

A: Let's find derivative of given  function.