4. If y(T) = 1 – exp(-bNT), find the inverse function T = T(y). (Show me your work!)

Q: 5. Find the first and second derivatives of y if y is a function of r defined implicitly by x* + y*…

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Q: Зх+1 a) y =- 1 b) g(x)= Vx -

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

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Q: Find the derivative of the function.

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Q: 1. Find the derivative of each of the following functions using chain rule: y=3x* (x* -2) a)

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Q: Find the derivative of the function f(z) = (3x +1)In(4x+3) %3D and then evaluate it at x = 0. f' (0)…

A: Given : f(x)=(3x+1)ln(4x+3)

Q: Find the second derivative of the function f(x) = 2 – 3x + 5æ/2 – 7e" . 15 f"(x) = –3+ 2 7e" 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: Compute the following derivatives using the chain rule. g(y) = ln(1 + y).

A: Take 1+y = t  And use chain rule

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: Compute the derivative of the given function. g(t) = 2t - In(2 – 5t) %3D

A: Given that: g(t)=23t.ln(2-5t)

Q: Find the third order derivative of y = In(cos(2x))³. A. y' = -40sec² (2x)tan(2x) B. y' = -80sec?…

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Q: 5. If f(x)= 5x² + 2x+1 is an invertible function, find the slope of the tangent line to f^(x) at the…

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

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

Q: 2. √√√x + y + xy = 21

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Q: Compute the derivative of the following function. 1(x) = 3e 3x f'X)%3D

A: Topic - differentiation

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: a) Calculate the derivative of f Cx) by first expanding and Simplifyıng the function fCx)=(2-3x) 2

A: Given,           fx=2-3x2

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

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Q: f. y=In(x8+1)

A: We will solve the problem

Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

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: 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: F(x)=In(52x+n • (x+2) ) %3D

A: Find the derivative of the function

Q: Find the differential of the given function y = xcosx

A: To differentiate

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

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Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x2 – 6xy + y3 = 24

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Q: Find the second differential of the function y=x2cos2x.

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Q: Find the differential of the function.

A: Differentials are infinitely small quantities. We usually write differentials dx, dy, dt (and so…

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: (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: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

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

A: The given function is

Q: In(4z+10) Find the derivative of the function f(z) = z'sin(9z + 12) + %3|

A: Given:- f(x)=x4sin(9x+12)+ln4x+10x3 To find:- Derivative of given function

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: Suppose h(x) =23r +1 What is the correct result of the derivative of h with respect A h'(x) =3-23x +…

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Q: Find the differential of the function. u = 2x + 7 du = %3!

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Q: Suppose h(x) =log,(3x+1). What is the correct result Зх + %3D of the derivative of h with respect to…

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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

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

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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: 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: Зх +1 a) y =- 1 b) g(x)= Jx -

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Q: 2-х Find the derivative of y = Зx+1 -7 бх-5 6- А. (3х+1)2 В. (3x+1)2 7-6х С. (3x+1)2 D. (3x+1)2 Е.…

A: Proceed as shown below

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

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