Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e5xy = sin (y³ ) (Express numbers in exact form. Use symbolic notation and fractions where needed.) SyeSty 5xey – 3, cos(y) dy dx II

Q: - a. Find the derivative of 3y – 2xy² = sin x + cot y b. Find the derivative of 2y x(3³) – In(²/²) =…

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Q: III. Find the indicated derivative of the following. 2. y +y x , y" 3. (x+ y)2 +(x - y)z = a , y" 4.…

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Q: Q3) find the derivative of each function: 1) y=x?sin*2x + x cos-3x 2) y? = (sin2x)* + (cos2x)* + 2xy…

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Q: - 9x Find the derivative of y with respect to x if y = e dy %3D dx

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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: 5cos3(x) Гу 3 sin(3–2x) + tan? (3x? — 4х) — csc(/2x — 1

A: Differentiate y w.r.t x.

Q: 13 Find the derivative of the function. Y = 2² + cos" (xx) a

A: Solution:- Given function is  y= a4+cos4(x)           ----------(1) Here, the variable is 'x' and…

Q: (a) Find the derivative of the following functions (i) y = a² sin“ x +æ cos-2 x. (ii) y = e(+v#+x²),

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Q: 1. Find the derivative d/dx using implicit differentiation of the following functions. Show your…

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Q: Calculate the derivative of y with respect to x. Express derivative in terms of sin (y³) (Express…

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Q: Use implicit differentiation in finding the derivatives of y with respect to x. What is the…

A: Given equation, x2 - 6xy + 3y2 =0

Q: Find the derivative of the following with complete solution A. y = sin x - 1 / cos x B. y = x^2 sin…

A: To Find the derivative of the following with complete solution

Q: Find the derivative of the following function. (3x² – 5) y = Cos z + (x² + 1)0* sin 5x

A: Given  y = 3x2-55sin5x + x2+1cosx

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos…

A: topic- derivative of a function

Q: 1. Find the derivative of the following: (Simplify your final answers.) f(x) = ev3(cos²zx) C.

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Q: cos (2x) Find the derivative of cos(e2«)

A: Given that: ecos2xcos(e2x)

Q: Find the derivative of the function at Po in the direction of A. f(x.y) = 5xy + 5y", Po(-6,6), A =…

A: Given  f(x,y) = 5xy+5y2  P0(-6,6) , A= 2i-j  .  To find  Directional derivative in the direction of…

Q: Find the equation of the tangent to the graph xey +y-2x = In 2. %3D Evaluate the derivative of the…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

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Q: 1. Find the derivative of the functions, do NOT simplify. a. y = In(8 – 3x) | b. y = ln /2.x + 1 3a2…

A: We have to pick the most challenging formula among differential formulas and solve it.

Q: Use the Chain Rule to find the derivative. y = cos (e40) (Express numbers in exact form. Use…

A: Given.

Q: 4) a) Determine the derivative dx of the following functions y = 3** b) 1-3- 3e² 1² c) y d) y =…

A: We have to find the derivative.

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 2 1. Z= 1+x? ; d²z/dx? 2. Y = (3x + 2)* ;y"…

A: Given function is: y=3x3+24 We have to calculate d2ydx2 or y''. Now we see,…

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: 1. Find the derivative of the following functions. (find y') a. у %3DIn(cos(20)) b. cos(xy) = x - y…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: 1. Applying the definition of derivative, a. find dy/dx in each of the following: 1 a. 1] y = - x² –…

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Q: 22. Find the required derivatives. a) y = (4x3 - 2x + 1)-2; find y b) x = Vy? + 1;find x"

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Q: 3. Use the Leibnitz formula for differentiation to find (i) for the function y=sin" xin) (ii) for…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Z=- 1+x? 2 ; d²z/dx? Y = (3x3 + 2)4 ;y" Y = V(2x + 1)2 yiv %3D

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Q: Find the derivative of y=2ecos.x)(sin(5x)) d'y Calculate as a function of t if x=t-t and y=t-t 2 dx?…

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Q: IV. Find the derivative of the given function. 1. u = t³(sin In t – cos ln t) 2. y = e-2* (1 + e-2x)

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Q: 4 a. Use implicit differentiation to find the derivative dy/dx of the given function. b. Find the…

A: The objective is to find the derivative and slope at the point .

Q: Find the differential of the given function y = xcosx

A: To differentiate

Q: Vw Find the derivative of y = 3W with respect to w. dy dw

A: To find dy/dw

Q: 1. 2x'y² + 4yx² = 6. Find dy/dx at (1, 1) by i- %3D

A: Here we have, 2x3y2+4yx2=6 ................... (1)  Differentiate with respect to x

Q: Find the derivative of the function at Po in the direction of A. f(x,y) = - 5xy + 2y. Po(-7,1), A=…

A: Given query is to find indicated derivative.

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

A: To compute the derivative of the function.

Q: Both x and ydenote functions of i that are related by the given equation. Use this equation and the…

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Q: Q3) Find the derivative of y for all functions the following (1) y 0 (sin (In 0) + cos (In 0)) %3D

A: Q3) (1) Differentiate with respect to Use chain rule to find the derivative of y

Q: 3. Determine the derivative of each of the following. a) y = e-*sinx b) y = 2* + 3* c) f(x) = xcos2x…

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Q: Find the derivative of y: 1- y = (cos 0)▼2

A: See the details solution in below

Q: Find the derivative d/dx using implicit differentiation of the following functions. Show your…

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Q: 7) Find the derivative y' using the derivative rules: a) y = 8xe 9x b) y = sin5 7x

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

Q: (b) Find the derivative of the following functions with respect tox. (i) y = sin (2x – 3) (ii) y = x…

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Q: 1 y 4 18) Find the first derivative of y = -sin? x

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Q: Q2) Find the derivative of the function at Po in the directi g(x, y) = x – (y²/x) + V3 sec-' (2xy),…

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Q: 2. In each case, find the derivative d. (a) z = x³ – y² and x(t) = cos 2t and y(t) = e-3t, (b) z =…

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Q: III. Find the indicated derivative of the following. 1. x? -4y? =5 , y"

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Q: I Find the second derivative(y") of the following functions and simplify the final result 1. y = x –…

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Q: Find the derivative of y with respect to x. y = sin -1(et) OA. 5e 5t /1- e 10t O B. - 5 e 5t /1- e…

A: We have to find