Suppose that f(x) I + 6 is differentiable and has an inverse for æ > 1 and f (2) = 8. Find (f ')' (8).

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: Consider y = f(x)=√1+2x, x 2-1/2. Without finding x = f(y) explicitly, find the derivative of the…

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Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: Use the u-substitution to find the anti-derivative of m'(x)= 1/xln(x)

A: solution :- antiderivative is the integration  So put ln(x)  = u Then (1/x )dx  = du And then…

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 second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: Prove that for all a, b e R, the function f(x) = 3x - 4x³ + 6x² + ax + b has exactly one point where…

A: f'(x) is increasing  function. But f'(x)  is polynomial of degree 3. So it has exactly one real root…

Q: Find the derivative of the function #1) F(x) = In(2x+3)· (4x +7) tan(x) t +4 dt t2 +2 # 2) h(x)= |

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Q: Suppose that f'(0) = 2. Find the derivative of the function (e2z – 2x)f(3x) at x = 0.

A: Given that f'(0)=2.Our Aim is to find the derivative of the function (e2x-2x)f(3x)-(i) at x=0.

Q: Find the derivative of f(x) = log, (x° + x – 1). %3D 2 + x - 1 f (2) = %3D (3z* + 1) (In 2) (3z +1)…

A: Given:     fx=log2x3+x-1

Q: Find the third Taylor's polynomial f(x) = x3 – x² + 3x + 1 which can easily find the derivative at…

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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: 18. If f (x) = es*, find (f-1)'(1) using Theorem 7 (Derivative of the Inverse Theorem).

A: We have to find derivative

Q: S-2(x-1 - x²) dx 5.

A:

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: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = π/4 , g'(2) = 5, and g"(2)…

A: singx

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: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

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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: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d.…

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

Q: Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈…

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Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

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

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Q: Find the differential of the function. u = 2x +

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Q: Compute the derivatives of the given functions. f(2) = In (7z²). 7a?). f'(x): / (z) = help…

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Q: Let y = f(x), where f(x) = x4 − 5x. Find the differential of the function.

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Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: If z = (x + y) ev and x = 5t and y = 1 – t², find the following derivative using the chain rule.…

A: We are given that z=(x+y)ey,  x=5t, and y=1-t2. Now, we need to find dzdt.

Q: 19.What is the derivative with respect to a of f(x) = 4-32 3z+2 4x-3

A:

Q: Find the differential of the function.

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

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 = (x + sin(x))³. Find g(æ) and f(x) so that y = (f o g)(x), and compute the derivative using…

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Q: If f (x) = In (4a + 1), then its third derivative is f(3) (æ) = %3D

A: In this question, concept of derivative is applied. Derivative The derivative expresses the rate of…

Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

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 second derivative of vx - Jy= 4 when x = 1. 2 1 -1 -2

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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: Match the functions in Column A with their derivatives in Column B. 1. f(x) = 4 А. f'(x) = 8x 2.…

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Q: Find the local linear approximation of f(x) = tan¯(x – 4) at xo = 5, where Ax = x – 5. Enter the…

A: Given: fx=tan-1x-4

Q: Evaluate the 3rd derivative of M with respect to (x) M= x6 y3 Cos (x6 y3) if x =6 and y= 3

A: The function is M=x6y3cosx6y3. Using implicit differentiation, find dydx.…

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

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Q: Find the derivative of g(x) = J2x u²+1

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Q: Find the derivative of f(x)=

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

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: 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))