• Find the derivatives of each of the following functions, telling me how you choose the rules you use, and showing your process. It might help to use the strategies shown in the videos to organize your work for multiple "chain links", especially if there are also other rules involved. f (x) = 3tan(5æ) o y = sint 2x cos 3x + sin 2x (). 4 f (t) = et In(3t)

Q: Solve for the derivatives of the following functions with complete solutions. Use a separate sheet…

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Q: For which of the following functions is the chain rule an appropriate method to find the derivative…

A: We have to find out

Q: 2. (a) This is correct. (b) This is correct. (c) This is incorrect. Because the differentiation is…

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Q: Calculate the first four derivatives of y = x- 1. Then find the pattern and determine a general…

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: 6. In(x³y²) = x² +y³

A: Let's find second derivative of given function.

Q: 1) Find the derivative of the function g(x) = (arctan x)3, first showing how to get the d formula…

A: As per guideline we have solve only one question

Q: B) Find all of the second derivatives for f(x, y) = (3xy2 + 2xy + x²) In; x²+y² itable graph and…

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Q: What is the derivative of y cos e4- 2 7

A: Solution is given below:

Q: f (x) = O(k) pmx) = f3) + 12f(x;2) + 39f(x,,) + 56f(x,) – 39f(x,-,) + 12f(x,_2) + f(x,_) 6h In the…

A: Given that, h=0.01, xi=4.00, xi+1=4.01, xi-1=3.99, xi+2=4.02, xi-2=3.98 The given function is:…

Q: 3. Evaluate the derivatives of the following: i. 2t +3 ii. x' sin x iii. In(3x-4) iv. (2x +5)"

A: i. Quotient Rule:  The Quotient Rule for differentiation is given by, Evaluate the derivative of…

Q: 4. Compute the derivatives of the following functions by using chain ru Describe your steps in…

A: Given: We need to find, ∂f∂w by using a) f(z)=exp-12zz=yTS-1yy=w-μ b) f(w)=tr(wwT+σ2IDxD) c)…

Q: 3 - 1 Find the derivative of y = - 3 with respect tox. tan A. 3 x +9 В. + 9 С. 1 x +9 D. x² +9 B.

A: Use given function find derivative

Q: Find derivatives of the functions defined as follows: y =(3x3 - 4x)e-5x

A: Given:          y=3x3-4xe-5x Let:  y=f(x)=3x3-4xe-5x Product rule of differentiation is given by…

Q: Q6. Find the first derivatives by using chain rule of the following functions: i. f(x) = tan %3D ii.…

A: Given that:                       (i) f(x)=tan1x(ii)g(x)=lnx3+x-1

Q: (x) =√1/x^3

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 10. Find the derivative of the following function. [Hint Using Chain Rule] a) F(x) = (x³ + 4x)? -5x…

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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: For which of the following functions is the chain rule an appropriate method to find the derivative…

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

A: Given.

Q: 2.6 The Chain Rule: If y= f(u); u= g(x), and the derivatives and both exist then the du dx composite…

A: Given y=f(u) and u=g(x) and dydu and dudx both exist.

Q: Q1-Find the derivatives of the following funetions using the defir 1. y=x-x 2. y-3/5х 3. y=x 4.…

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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: 1-2) Use the 4 step process or the increment method to get the derivatives of the following…

A: 1) y=4x2+3x2) y=2x-13) y=4x4+2x3-3x2+7x-15

Q: 1. Find the derivatives of each of the following functions. 3x + 2 (a) g(x): (b) f(t) = (tan t)³ (c)…

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Q: Evaluate the derivatives of the follow separate sheet of paper. 1. у%3 4x — 7 2. y = cos(x) + 4x 3.…

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Q: 5. Given b(x) = (3x – 7)*, if m(x) = 36 (2 tan-1 (1 – 7x)) then m' (x) is %3D %3D

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Q: Determine the third derivative of y = In(2x + 3) Determine the third derivative of y = e(-x²/2)

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Q: 1. Find the natural domain and the derivative of the given function. (a) 3x² +7x + 5, (b) (3x +1)5,…

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Q: Physicists sometimes have to compute derivatives of the following form: (1) o2 – 1 do do Use the…

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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: 13. Let m(x)= f (*)-k (x), find m' (-2)

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Q: We want to find functions u₁(x) and u₂(x) such that yp = U₁Y₁+U₂Y₂ is a particular solution. We can…

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Q: f (x) = x² + 2* – 100 Solve this question by the Fixed-point method on the topic of solution of…

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Q: Find the derivative of: h(x) = (1/x^2 - 1) / (1/x -1)   (1/x -1)^2 –1/x^2 (1/x^2 – 1)^2 (1/x +1)^2…

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Q: Solve for the derivative of the given functions using the Chain Rule formula.Let g(x) = sin (cos…

A: Since, g(x)=sin (cos x)g'(x)=cos (cos x)ddxcos (x)⇒g'(x)=cos (cos x)(-sin (x))ddx(x)⇒g'(x)=-cos (cos…

Q: Find the derivatives of the following functions. Do not simplify. (a) f(x) = ((3x−5)(−x^−2…

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Q: 1. Find the derivatives of the following functions using derivative rules from Sections 4.3/4.4.…

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Q: 1. Find the derivatives y = x' /4x -1 y =- y= (2x + In x)? V1-2x 2. If f(2) = 4, f'(4) = 6, f'(2) =…

A: We will use the formula (uv)' = uv'+u'vuv' = vu'-uv'v2(f(x)2)' = 2f(x)f'(x) 1) Consider y = x24x-1y'…

Q: 3. sin 2m 5. 17 20 M(x) KER 27 (2x+ 1)m 2m sin 10 * 17 xS 13 11(2x 20 37 33 7. 13 <xS 24 where M(x)…

A: According to our policy, we solve only the first three subdivisions. For the remaining subdivision,…

Q: Q 1. Hello, I am struggling to do my derivatives  calculus homework. I need help on this problem…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

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Q: 3. Compute the following derivatives using the chain rule: [f(g(x))] = f'(g(x))g'(x). In each part,…

A: Given: a) ddxln(cosx)b) ddxxex

Q: f(x) = e²x cos(x)

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Q: IV. Find the derivatives of the foll 1. y=-10x +3 cos x 2. y xcos x

A: 1. y=-10x+3 cosx2. y=x2cos x3. y=sec x+tan xsec x-tan x4. drdθ if r=secθ cscθ

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given that, the function f = xy2(z3 - 1) We need to find that  g(x, y, z) =  ∂f∂x + ∂f∂y + ∂f∂z

Q: Example: 1. Find the derivative with respect to x for the following. a. y= e3x2-1 b. f(x) = ee c. y…

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