2. Use the definition of the derivative to find the first and second derivatives of the function. 1 f(x) = %3D 1- x You should get f' (x) = and f"(x) = 2. %3D (1-x)2 (1-x)3"

Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: Find the derivative of the function. y = x°cos x - 10x sin x - 10 cos x

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Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

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Q: Find the first derivative of the following functions Y = x5 e-3 ln x and Y = ln √ [ (x – 1 ) / ( x…

A: Solution is given below:

Q: The derivative of y = 2 ln ⁡ x − ln ⁡ x 3 is

A: The given function is, y=2lnx-lnx3

Q: Find the derivative of the function. f(x) = 4 3 VX + 2cos x

A: Here, the given function is: f(x)=4x3+2cos x

Q: 4) Find the derivative of the function: x* cos x h(x) %3D Vx2 + 1

A: Answer

Q: 5. Find the third derivative of the function : 3 (ans. : - 8y y=Vx

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: What can we use to find the derivative of a function when it is impossible or difficult to isolate y…

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Q: Find the derivative of y=ln[x^3(x^2-5)^3/4]

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Q: 12) Find the first derivative of f(x) = 3x %3D

A: Use rules of derivative

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

A: (4) Consider the given function. fx=2cosxx2 The quotient rule is defined as. fxgx'=f'g-g'fg2

Q: 14. f(x) = 2 +3cos x

A: using basic properties and application of derivation we will solve this question.

Q: y = (Arccos 3x³)³

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Q: 1 Find the function whose derivative is (x+1)-

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Q: Find the derivative of the function. y = 3 tan(x - V1 + x 1 + x2 y' = ||

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Q: Find the derivative of the function .

A: Given a function f(x)=2x3+3 cos x f(x)=2(x)1/3+3 cos x      =2x-1/3+3 cos x We, use the following…

Q: Find the derivative of the function. y = 3 x tanh-1 x + 3 In/1 - x2 y' =

A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

Q: 1 14) Use the definition of derivative to find dx 3- х.

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Q: Find the derivative of the function. Y= q56* In(2)ln(5)ln(6)· 3*. 5".; 2:56*+1+x

A: Given problem:-

Q: find th first derivative: x=2cos2 t/2

A: we need to find the first derivative of

Q: Example 2: by using the definition of the derivative, find dy/dx of the function y = 5x + 8x - 3x +4

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Q: 1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

A: To find the derivatives of the given functions.

Q: What is the derivative of: y ln x − x ln y = 1

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 6 Find the 3rd derivative of y = (x-1)2

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y)=xy, What is…

A: To find the derivative of y with respect to x

Q: a.) z= 5.

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

Q: 22 Find the 43rd derivative of (1 + x²)“ at x = 0. 0.

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Q: Find the derivative of f(x) = –4 ln (5 cos (-4x))

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Q: Example 2: by using the definition of the derivative, find dy/dx of the function y 5x' + 8x - 3x +4

A: We can use definition of limit In order to solve the given problem.

Q: 2 Find the derivative of y = arctan(x´ + 3)

A: We have to find the derivative of the given function.

Q: 4 Find the first derivative of y = In X +

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Q: Find the derivative of y = csc¯(In sin (x))

A: use simple integration formula.

Q: 5. Find the first derivative of y = (2x³ – 1)5 Vx² – 1

A: Given: y = (2x3 – 1)5√(x2 – 1)

Q: 1) Find the derivative. Simplify where possible. y = x tanh-1x + In/1 – x²

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Q: 2. If f (x) = xV x + 3, find the derivative of this function and the slope of the tangent line at…

A: Product rule of differentiation: (fg)'=fg'+gf' The slope of a tangent line at (a,b) is given by:…

Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

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Q: 1. Find the first order derivative of u = x*.

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Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: 2. Find the derivative In (x+) y3=

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Q: c. Find the derivative of y =+- et x3 cOS X 2

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Q: 1. Find the second derivative of y = sec-'x+ csc-!x. a. 0 b. C. +x+ d. -1 2. е.

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Q: Find the first derivative of h(x) if h(x) = cos (x – 2x) -

A: h(x) = cos2(x3-2x)

Q: Find the derivative of the function. 10 f(x) = 3 + 4cos x %3D

A: Given that fx=10x3+4cosxTo find its derivative

Q: 2) Find the first derivative of y = sec1(2e3*)

A: To find the first derivative of the given function.

Q: Find the second derivative of y=x-1 at x=2

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Q: 1) Find the derivative of the function: (3х — 1)3 Vx* — 1 f(x) = cos² x

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