Activity 2. Find (a) y by equating the function to y and differentiating it; (b) y' by implicit differentiation; and (c) y" using either of the solved y'. 4. (x + 2y)? = 4xy + Vx 5. x3 - y3 = 3

Q: 1. Find the derivative of the following e)y ln x - x ln y = c

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Q: 3. Find the first and second derivatives of the function f (x) = e¬²

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Q: 1. Find the second derivative of the function. 8(x) = 3\/x + e7*In(x)

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Q: diy in terms of x and y. dz² ニ 86

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Q: 4) fip by implicit differentiation, where Find dr y + x?y³ = x* + y.

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Q: 9. [Essay] Find the derivative of y = 3x + 1). За* (x? — Зх + 1). Зах

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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: 20. Find the derivative of the following functions (do not use exponential definitions of hyperbolic…

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Q: y = V4x² + 5x

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

A: The implicit function is of the form f(x,y)=0 in implicit differentiation y is a derivative of dydx…

Q: 4. The equation (x – y)² = x + y – 2 defines a function y = f(x) in a neighborhood of (1,2). Use…

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Q: 5. Find the 25" derivative of y= In x. 6. Find the 100 derivative of y=e".

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Q: 2 Suppose that x and y are related by the equation 4x² - 3y² = 5 and use implicit differentiation to…

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Q: Find the equation of the line that is tangent to y = ln x at x = 1.

A: Find the equation of the line that is tangent to y = ln x at x = 1.

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: c) Use Leibnitz's Theorem to calculate the 4th derivative of y = x^sin (3x) d) Locate and identify…

A: We have to solve part c and d.

Q: 11. Consider the equation x + y +e# = e dy using implicit differentiation. dx (a) Find (b) Find the…

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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: -1 Find the derivative of the function: y=6 sin ¹¹ (x²). y'= y'= O y'= 12x y'= -X 2x 2 + X 12x 4 4 X…

A: Given y =6 sin-1 (x2 )

Q: 3.8 Implicit Differentiation .) Use Implicit differentiation to determine dy 3 4 given the equation…

A: Given: x5+y3=5Differentiation formula:ddxxn=n.xn-1ddxc=0

Q: 1. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Part 1 : Slope of tangent at (π2, π4) is given by dydx(π2, π4) ⇒y·sin 8x=x·cos 2x⇒ddx(y·sin…

Q: 1. a) Find the derivative of the function y = sinx + cosx. %3D b) What is the value of the…

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Q: 2. Find the derivative of (x + 1) /x. 3. Given the equation: y = (eln )?, find y'.

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Q: -1 The derivative of the function y = sin Va at 1 is equal to 4

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Q: 2 cos x 4. Consider the function f(x) = x2 find its derivative

A: Given function: fx=2cos xx2Differentiate the above function w.r.t 'x' f'x=ddx2cos xx2

Q: Q. 2. a) Find nth order derivative of f(x)= ln(2x-7). b) Find 3rd order derivative of y with respect…

A: The function fx=ln2x-7. The first derivative of the function fx=ln2x-7 is computed as follows,…

Q: (12) Find the derivative of the function Y = cos (a³ + x³)

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Q: a.) z= 5.

A: We will find the second derivative of the given function in the following step.

Q: 2. y = a Cos-1 (1 -2) + V2аx — х2 a

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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: a) Find implicitly, if y°cosy +x = 2xy b) Define differentials also find derivative by using…

A: (2)(a) We have the given function as y2cosy+x2=2xy On using implicit differentiation, we get the…

Q: a) Find the derivative of y = 2 sin-1 x. b) What is the value of the derivative at x = 0.

A: given

Q: 2. Find the equation of the tangent line and normal line to the curve f(x)= 3x at the point(1,1). x²…

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Q: Find the first derivative of the following: 1. y= y = Ine-tanh² 2x 2. Y= sech(5x-1)tanh(5x-1) 3.…

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Q: Activity 1: Find the derivative of y with respect to x. 1. y = 3x - 5 2. y = 6 3. y = x2 + 4x 4. y =…

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

Q: Find y" by implicit differentiation.   x3 + y3 =1

A: We find y' first

Q: 5- When the first derivative of the y = sinx function at x =pi/4 is calculated with the forward…

A: We will use basics of numerical methods here

Q: 3. Find all possible functions with the given derivative y' =- 2

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Q: x³ + 3y = xy (By implicit differentiation)

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Q: Consider an oscillating mass that weighs 3100 grams which is attached at the end of a spring with…

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Q: 6. Find y"by implicit differentiation of x³ + y3 = 1.

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Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 %3D dx b) EVALUATE THE DERIVATIVE FROM PART a AT…

A: Given: x4y3=-8

Q: 1.) Find the area under the curve y = x3 + 3x2 and the axis between x = 1 and x = 3.

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

A: Let z= 6x^2+1 Substitute that. Then take d/dx on both sides.

Q: 9. [Essay] Find the derivative of y * sign 3a* (x? – 3x + 1).

A: Given function is: y=3axx2-3x+1 We have to find the derivative dy/dx. We will use the following…

Q: e) The function f(x) = log(x)log(x) with x %3D Jse fzero to find a zero of its derivative. What is…

A: The given function is f(x)=log(x)log(x); with x≥1

Q: ■ Find y 2    implicit differentiation.   x4 + y 4= a4

A: Givenx4 + y4 = a4differentiate with respect to x4x3 + 4y3 dydx = 0dydx = -x3y3 — 1Differentiate with…

Q: e2x 2. Find the derivative of y = - (x² + 1)°(1 (1+ sin x)5

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Q: Can i get help step by step please

A: We have to use the power rule because of exponent -1 and then use the chain rule for (cscx-cotx).