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

Q: 2. Calculate the derivative of the following y= (*- 3 + Sx) B. Ytan (x+ Se-2) (4x + 3) Tx-2) A. C.…

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

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Q: find the n-th derivative of f(x). f(x)=e^-2x

A: Given function is fx=e-2x. Chain rule of differentiation states that: ddxfgx=f'gxg'x Now, we find…

Q: Q1:- Find the first order derivative of each of the following functions: e) y = 1 + x'nx

A: Given that y = 1 + xlnx . We find its first derivative. We know that d(xn )  /dx = nxn-1  Here i…

Q: 3 Find the derivative of f(x) = x°e*.

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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: 13. Find the derivative of y = ef 2e D.y'= A. y' B. y' = - C.y: cy-

A: The function is y=e2x

Q: Find the derivatives of the functions in Exercise

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Q: 1. Find the derivative of each function. i] f(x) = e*=*

A: Here f(x)=ex2-πxddxf(x)=ddxex2-πx=ex2-πx ddxx2-πx=ex2-πx 2x-πHence, ddxex2-πx=ex2-πx 2x-π

Q: 1. Find the derivatives of each of these functions: a. y = ln (4x² + 4) b. y = 22² c. y = 25x+7…

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Q: 1. Determine the derivatives of the following functions (a) y = (x² - 2)²

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the fourth order of derivatives of the following functions y=ln x y= X^1/2

A: The objective is to find the fourth order derivative of rhe given functions.

Q: Find the derivative of the function. 1 + e5x e 5x 3x e

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

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

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: 4 Find the derivative of the function y= f(x)= Jx(x-8). %3D

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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: Find the second derivative of the function. f(x) = (3 + 2x)e−3x

A: Given:The given function is f(x)=(3+2x)e-3xTo find:The second derivative of function f(x)

Q: Find the function with derivative f'(x) = e8 that passes through the point P= (0,7/8).

A: We are given a diierentrial equatrion[f'(x)=e8x ] and a pssing point (0, 7/8) of the same  we need…

Q: h(x) = e(-1/2)x

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Q: Find the derivative of f(x)=(x+4)e^(5x)

A: We have to find the derivative of f(x) ,where f(x) is given by

Q: Find the SECOND derivative of the given function. (b) g(x) = x+2

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Q: Find the derivative of the function.

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Q: 24// Find first and second derivatives of the function (3xy + 7)2 = 6y.

A: Step:1 We have to find the first and second derivatives of 3xy+72=6y Here we have to find the…

Q: 9. Find the derivative of y = xe3-x (A)e3-x? (B) 0 (C) e³-x*(1– 2x?) (D)–2xe³-x² (E) e3-x*(1+ 2x²)

A: Given : y = xe3-x2

Q: What is the derivative of y = (x2 + 1) e-3 ? O y = (x² +1) (e-3) + xe² - 3 O y = (x² +1) (e*-3) +…

A: It is required to find the derivative of the given function.

Q: Find the first and second derivatives of the given function. f(x) = e *(3 + 3x)? Calculate f'(x).…

A: The given function is fx=ex3+3x2

Q: 2. Find the derivative of each function. # 45 : y = In(1+e2") b. # 47: y = a. et +e-a

A: Chain rule: If F(x) is a composite function f(g(x)) and if F(x) is differentiable, then the…

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: 11. Find the derivative of the following function. y=2-6e a y'=54r°e b. y' = -54x°e- c. y' = 6e d.…

A: Given function is

Q: 11 8 Find the derivative of the function: y = 3(x – 4)' x-4

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Q: Find the derivatives of the functions k(x) = x2 sec (1/x)

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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: g. y = x e 2x h. y = 4sin 2x

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Q: Find the derivative of the function m: f(x)= e^x^3+4

A: Topic = Derivative

Q: Find the derivatives of the functions y = (1 + 2x)e-2x

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Q: Find the first derivatives of y = x3 – x + 2 e*

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Q: 1. Find the derivative of the function y = (x² – 1) (2x² – 3). | 2. Differentiate g (x) = x+1l x+2 °…

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Q: Find the first derivative of g(x) if g(x) = e²* In(2x) %3D

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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 first derivative of the following implicit function: X² + 3xy + y² = 4

A: Given : x2+3xy+y2=4 Lets take first derivative  Take derivative with respect to x. apply the power…

Q: a) Find the derivative of the function: T+ V3x f (x): 3x-1

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: 2. Find the derivative of (a) f(x) = x* + 3x 2+ 4e" 4 (b) f(x) = 2 tan(x)- 2"

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the first derivative of the following implicit function. x² + 3xy + y² = 4

A: Given : x2+3xy+y2 = 4

Q: Find the second derivative f"(x) for f(x) = e(#+2)*.

A: First calculate the first derivative for f(x) using the chain rule.…

Q: 3. Find the derivative of y = | (12 +1) dt.

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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: Find the function with derivative f'(x) = e7¤ that passes through the point P = (0, 6/7).

A: Given that f'(x) = e7x and we find function that passes through point (0,6/7). We know that f'(x) is…

Q: Determine the value of the derivative function for Ax) = (x + x)(x- 2) at x = 2. %3D A 6 в О с 5 D1

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