Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

Q: Find the differential of the function T = uw / 1+ uvw

A: Our Aim is to find the differential of the function:-T=uw1+uvw-(i)

Q: Part 4: A derivative computation using the FTC and the chain rule d d (F(2*)) = dx dt |3| e dx 20

A: Topic:- application of integration and derivatives

Q: Calculate the derivative e12x d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus.

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Q: Find the first derivative of y with respect to x for the following :functions b- y = In( 3x .e-*)

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Q: Find the derivative of y with respect to x if y = 4Vx(2x + 3). D. E - А. 6(2x+1) 3 B. C. 12V1 + 6 O…

A: Given: y=4x2x+3 ⇒y=8x32+12x12 Since, we know that ddxxn=nxn-1

Q: Find the first order derivative with respect to y of the function u = log(x + x² – y2)

A: Using derivatives.

Q: Find the derivative of the function. y = In(e7x + 5)

A: Given y=ln(e7x+5)

Q: Find the derivatives of the functions in Exercise

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Q: 1 y = x²-1 Using differential, draw the function

A: This is a problem related to differentiation. Based on the general formula and concept we will…

Q: 1 y = V2x+5 /2х+5

A: By see this solution

Q: Find the differential of the function. z = 3t - = zp

A: Differentiate the function: - Differentiation is that the quantitative relation of a small amendment…

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: fx=sin-1x,   a=π12 The value of the function and the value of the derivative can be easily…

Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

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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: Find the derivative of the function.

A: Some important derivative formulas: 1. d(lnx)/dx = 1/x 2. d(√x)/dx = 1/(2√x) 3. d[N/D]/dx = [D*(N)'…

Q: Consider the derivative function h (x) = 5x³ + 3x² – 4x + 4. What is the general antiderivative of…

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Q: Find the first and second derivatives of the functions w = ez(z - 1)(z2 + 1)

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Q: (3) Compute the derivative of the function e2t cos tdt.

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Q: Find the linearization of the function f(x) = sin(x) at a = π and use it to approximate the number…

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Q: In (xv/x² + 7). n (xVx2 %3D · Find the derivative of the function y = In

A: To find the derivative of the Given function, we have to apply chain rule and product rule.

Q: Find the derivative of y with respect to x. y= sin -3 O A. XV1-x - 3 O B. 1+x - 3x 3 c. 1-x -3 O D.…

A: Given that: y=sin-11x3

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 – 7x³ + 21x² - i) y = (x² +…

A: As per guideline we have to solve first three subparts

Q: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.

A: Given x>0, The differentation of natural log x is 1/x  And differentation of constant are zero.

Q: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

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Q: Obtain the derivative of the function y y = (e*1) (In(2cos(x² – 4x))

A: The given function is: y=e3x+1ln2cosx2-4x

Q: The derivative of the function y = tan(In(vx2 –- 6x + 1)) is: |

A:

Q: The derivative of the function y = x² In(x + 1) is:

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Q: Find the differential dy of the given function.    y = x tan x

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Q: Find the first derivative of with respect to x using the increment method y=3x^2-7x+12

A:

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: %3D

A: Formula:ddx(tan x) = sec2xddx(ln x) =1xddx(xn) =n xn-1

Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

A:

Q: h(x) = In (2x-2)+(x² +1)e³x-6 %D Calculate the derivative at x=2, that is h'(2)=

A: calculate the derivative as shown below: h'x=ddxln2x-2+x2+1e3x-6…

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

A:

Q: (x3-x)² .3. 2 5. у 3 х+1

A: We’ll answer the 5th question since we answer only one question at a time. Please submit a new…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. In x 20) у 3

A: Given

Q: Let y = f(x), where   f(x) = 5x3/2 + x1/2.   Find the differential of the function.

A: The given function is

Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 17) y =x*in x -x3 A) 4x3 - x2…

A: Given, Find derivative of y=x4lnx-13x3 with respect to x

Q: Suppose g(x) = = A, and f' (1) = B. Find the derivative In(In(In(f(x)))), %3D f(1) = dg dx \x=1…

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Q: Find the differential of the function. u = 3x4 + 4

A: The given function u=3x4+4

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

A:

Q: Find the derivative of f(x)=

A: We use the quotient rule of logarithm to simplify the expression

Q: Find the 1st and 2nd derivatives of the following profit function: =(xa-110)1/a that is, and find…

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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: Find the derivative of the function. y = In) x +6. (a)"* g(x) = log,(x) 9'(x) = (b) y = x5x + 2 (c)

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Q: Find the derivative. COSx a) f(x) = In %3D x2-4 4 b) g(x) = Vx + e2x + Tt

A: Given : (a) f(x)=ln(cosxx2−4)

Q: 2. Find the derivative of h with respect to u if h = n²u

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Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

A: