1. Find the derivative (dy/dx) of the following functions: a) xy = cot xy b) x cos(2x + 3y) = y sin x c) cos y + cot x = xy

Q: Find the derivative of y with respect to the independent variable. COS y = 10 cos ( OA. -10 COS TO…

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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: Show that the function e (cos y +i sin y) is holomorphic (anal ytic) and findits derivative.

A: u(x,y)=e^x*cos(y) and v(x,y)=e^x*sin(y) We prove Cauchy Riemann satisfy everywhere

Q: Find the derivative. sin 0 d. 1 dx 1- x2 de A. tan 0 B. sec 0 C. cot0 O D. cos 0

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Q: Show that the function f(z) = e* – y?(cos(2xy) + isin(2xy)) is entire and find its derivative

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Q: Show that the function ex(cos y +i sin y ) is holomorphic and find its derivative

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Q: I. Find an equation of the tangent line to the graph of t cosh (f² – 1) dt tan-l † | f(x)%3D /1+ln…

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Q: Find the line tangent to the graph of f(x) = cos(x) at xo = T.

A: f(x)= cos(x)  Then, f(π) = cosπ⇒f(π) =-1

Q: 1. Find by implicit differentiation (a) e=/y = x – y (b) sin (x + y) = COs r + Cos y

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Q: Find the tangent line to the curve x cos y + y cos x = 1 at (0,1). O A. (cos 1)æ + y = 1 O B. x + y…

A: We can find the tangent line as below

Q: Compute the derivative for r(t) = (cos(8t))i + (sin°(t))j + (tan(6t))k.

A: Derivative of r(t) = cos (8t) i + sin9(t) j + tan (6t) k

Q: 3- Use implicit differentiation to find dy B- Xy= Cot (xy) y Sin()=1- xy

A: In implicit differentiation, differentiate each side of an equation with two variables by treating…

Q: Determine the points in the interval (0, 2T) at which the graph of the function below has a…

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Q: The equation of the tangent to the curve y=4+ sin' x at X=0 is O y = 4 O y = 2 O y = 6 O y = 3

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find of the fo lloming function the derivative Tin C A y'= (Sinsc) oc Sin 6-1 Sinac +Inx cos scl +…

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Q: Calculate the derivative of the following function. y= cos (6 sin x) dy %3D dx

A: Given that        The function is y= cos(6 sin x) Here we have to find dy/dx .

Q: 2. Find equation of the tangent line at the point P given by t = where x(t) = cos (t) %3D y(t) =…

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Q: Find the derivative w = sin* y cos*y a. sin³ 2y cos 2y b. sin² 2y cos 2y c.sin 2y cos 2y d. sin 2y…

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Q: Find the equation of the tangent to the curve at t = 0

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Q: Consider the curve given by cos(x)+cos(y)+2x+y=2. Determine dy/dx for this curve using implicit…

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Q: Can i get help step by step please

A: Consider the given function

Q: Find the derivative dydx of the cardioid given by the equation r=f(θ)=a(1+cosθ).

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Q: Find the derivative of y with respect to x. y = In (tan -1(2x4)) dy %3D dx

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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: d (cos x) = - sin r. dx %3D Prove, using the definition of the derivative, that

A: y=cosxsinx+1

Q: Suppose that y is a differentiable function of x and w = sin(y2). Express the derivative of w with…

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Q: Prove that d/dx(cos x) = −sin⁡ x using the definition of the derivative.

A: Given: fx=cosx   As we know from the definition of the derivative; The expression for the derivative…

Q: Assume that y= sin dy 'x is a differentiable function of x. By differentiating the equation x= sin y…

A: Given,           Assume that y=sin-1x is a differentiable function of x. By differemtiating…

Q: If x cos' 0 y = sin' 0 dy • the derivative dx and %3D (A) tan' 0 (B) -cot 0 (C) cot 0 (D) -tan e (E)…

A: Given: x=cos3θ and y=sin3θ To find: The derivative dydx

Q: Find the derivative of y with respect to x. y = sec 1(3x? + 1), x>0 dy dx II

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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: If f(x.y)=sin (2x+y) then the derivative f, Is 2 cos (2x+y) a. b. cos (2x+y) c. 2 sin (2x+y) d. 2…

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Q: The third derivative of y = cos 1 sin 27 1 111 a) y" b) y" 27 %3D 3 1 1 c) sin d) y 27 y = - %3D 27…

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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-…

A: Given problem:-

Q: The derivative of the function y = sin VE at a = is equal to %3D 4 14

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Q: Find the derivative dy dx || dy dx of the function y = sec (₁ +√4+ sin ¹(4 + ²))

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Q: The third derivative of y = sin(2.x) is (A) None of the given choices B y" = 8 cos(2æ) © y" = -8…

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

Q: 14. Find the derivative of y = e cosz %3D A. y' = -ecosx sin z B. y' = elinx cos x C. y' = -etinx…

A: Given,y=ecosxdifferentiating both the sides w.r.t. xdydx=ddxecosxUsing chain…

Q: 1- find dy/dx as a function of x. y = sec (tan x)

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

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: Find the value of the derivative of g (x, y) when we restrict to the curve defined by x = cos t and…

A: Differrtiate with respect to t

Q: Let y be defined implicitly by the following equation as a function of x and z : eyz +sin(tyz) – xyz…

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Q: Find the derivative of y = Arccot (tan(esecx)) in its simplest form %3D A. y' = e Sec*secxtanx B. y'…

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

Q: 11) Let r = sin 0. dy (a) Find the derivative dr (b) Use part (a) to find all distinct (r, 0) points…

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Q: a) Differentiate implicitly to find for the equation x cos y = x2 y2 +1 dx %3D b) Find the equation…

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Q: The derivative of y = In(sin(ex + 1)) is O y' = -ex cot(ex + 1) the above y' = -ex tan(ex + 1)

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Q: 16. Use Implicit Differentiation to find an expression for dy/dx given r*y² + cos(y) = 1. %3D

A: Given: x3y2+cosy=1   We know that; The Sum rule: f±g'=f'±g' The Product rule: f·g'=f'·g+f·g' The…

Q: 3. Find the derivative of (a) f(x) = (x+ 4 sin æ) (1 – 6 cos a), an (b) sin r g(x) %3D 6x

A: a). Given function is fx=x+4sinx1-6cosx. To find the derivative of given function. Solution: Product…

Q: 3- Use implicit differentiation to find dy 2 B. Xx-Cot (xy) y Sin f )=1-xy 2

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Q: dy if Use implicit differentiation to find dx a* + /tan y = x In y %3D

A: We need to find dydx for x4+tan y=x ln y. So,                x4+tan y=x ln yDifferentiating both…