6. Given that g(x) is the inverse of f(x)... f(x) = 3x + Vx + 3; find g'(2) a.

Q: 1 dt. o t4 +5 Let f(x) = Find the derivative f'(x). e2x none of the choices et

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Q: 4. Find the second derivative for the following functions : a) y=(x+!)' (ans.:6x +6+ 12) x' b)…

A: (a)

Q: Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

A: ANSWER :

Q: Find the function with derivative f′(x)=e^3x that passes through the point P=(0,8/3) f(x)=

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Q: 2. Find the derivative of the following functions. (a). g(x) = cos (2x + 1) (b)," f(x) = In (x² – 4)…

A: To find the derivative of the functions

Q: Find the second derivative of the function y=x(x² – 1)² A) None of the given choices B) 2x(5x2 - 6)…

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Q: 1.2 s Find first derivative for the following functions. dx (a) y = 5+ 6x + 4x3 (b) y = In(2x) +x*…

A: Note:-Since you have asked multiple questions, we will solve the first question with three sub-parts…

Q: Find the derivative of f(x) = In(e +4) 1 O 3e? e+4 3e3

A: We use the chain rule

Q: 3. Find the derivative. sh (a)l= - पक) (a) f(x) = x2 cos x +x tan r (b) h(x) = e" (x² + 4x) %3D t2…

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Q: If f(x) = and g(x) = Vx, then the derivative of f(g(x)) is -VE (A) ( + 1) (B) -(x + 1)- -2x (C) ( +…

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

A: Given that a function f(x,y) is continuously differentiable on an open region, we can derive the…

Q: Answer the given problems in two ways: (1) by using Chain Rule (2) by finding f(g(x)), taking the…

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Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+ 1)

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Q: Find the second derivative of the function y=x(x² – 1) (А) 4x(5х2 - 3) в) 2x(5x2 - 6) (с) (2х -…

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Q: Find the second, third, and fourth order derivatives of: y= f(x )= ax7 + bx3 + c y= f(x) = 3x/1-x…

A: It is simple derivative

Q: c) h(x) =(5x-1) 12x² – 6 d) m(x) = (4x² – 9x} %3D

A:

Q: 4- Calculate the second derivative of the function y = f (x) defined by the equation x³ + y3 +3xy +…

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Q: (1) (a) Find the derivatives of functions f(x) = e2 and g(x) = 5æ?. (b) Compute the definite…

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Q: 20. Find the derivative of the function. y = 9cos(2x) a. y'=-18sin(2x) b. y' =18sin(2x) c.…

A: Option (a) is the correct option. Differentiate y using the chain rule.…

Q: e3x-e-3x Y = e 3x+e-3x 4. t2 y= 72-1 5. X = t-1

A:

Q: 2 3 1. Determine the derivative to y² = x³ + y² + 2xy

A: Given problem:- Determine the derivative to y2 = x3 + y3 + 2xy

Q: 1 Find the derivative of the following function: f(x) = e2X(3x² - vx) 2e2X(6x - 1/x) O e'(6x -…

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Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (ans.: (3x-2) a)…

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Q: 1) The derivative of f (x) = e2x² cos x is: 2) Simplifying the expression e n(4x-3) + eln 2x In(e3x)…

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Q: 7. Find the first derivatives of each of the following: a. y= 10x³ – 4x² + 6x – 12 b. g(x) = x'e" c.…

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Q: B. Find the first and second derivatives of the following: 1. m(x) = 2(x)(√x) 2. a(x) = √3x 3. [u(x)…

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Q: 10. Find the derivative of the following function. [Hint Using Chain Rule] a) F(x) = (x³ + 4x)7 d) y…

A: The chain rule says:ddx[f(g(x))]=f'(g(x)) g'(x)=d[f(g(x))]d[g(x)]·d[g(x)]dx   Note: According to the…

Q: Find the third derivative of f(1)= 2x(x -1)" Oa 18 b.14cos 13 OC16sim Od12

A: we all know that dxndx= nxn-1. and first derivative dfxdx=f'x and second derivative df'xdx=f''x and…

Q: 3. Find the second derivative of f(x) = 2sin²(3x) а. 36сos? (3x) — 36sin? (3x) b. 36сos (3x) —…

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Q: 3 Find the derivative of the inverse of f(x) = x +1 using the formula dy %3D 1 off "(x)= g'(x)= dx…

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Q: 4. Find the second derivative for the following function a) )* 22 y3(x+ (an b) f(x)=/2x + at x= 2 c)…

A: See the attachment

Q: 3 Suppose 8 (x): 2(1- 5x)3 .What is the correct result of the derivative of g with respect to x? 45…

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Q: 1. Find the derivative of each of the following functions a) f(x) = cos5x %3D b) g(x) = cos 5x c)…

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Q: 1. Find the anti-derivative of the following. e" (x + 1) dx x2

A: From the given information. Anti-derivative has to be calculated to the following expression.

Q: 1. Find the first derivative of the following functions: y = f(x) = -(2x + x³)-2 + 4x (2x+4)² (a)…

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Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

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Q: Find the first derivative of y with respect to x (y') of the given function. y = ((U^2 - 1) / (U^2…

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Q: Which of the following is the derivative of the function f (x) = 5x · e*? Of (x) = 5e* Of'(x) = 5e*…

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Q: Find the derivative of the function f(x) = Jet – In(/x) (e+12 – 1) O (e:/2 – 1/x)

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Q: 2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of…

A: Since you have posted multiple questions, as per our guidelines we are allowed to answer the first…

Q: 8) Find the derivatives of the following: a) f(x) = 4e* – 2x + 5 b) f(x) = ln 2x² c) f(x) = (4 – x)5

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Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

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Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: 25. Find the derivative of the function. y = (1+ 3x)e - 3x O A. - 9e - 3x 3x В. - 3(1 + 3х)е - 3x -…

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Q: Find the derivative of the function: y = In e+2*+1 Oy = x"[(2x(ln x + 1) + 1] y = x*(2 + x + x² In…

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Q: 11. 5 4 Determine the derivative of y=x° – x* + 6. - Enter your next step here dy ab a + JT 00 () dx…

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Q: 1. Find the derivative of the following by using the Theorem. a. y = In(3x3 – 6x +9) b. y = In[(2x –…

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Q: Find the derivative of the given function. e5x (2x+1)5 f(x) = In Vx2+1

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Q: 7. Find the second derivative of the following function: y = e** +In(7e¯* + 5x³) – 5²× +-

A:

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.