Show that the derivative of ! log (9-1)(g-1)u²+2u–1 u e [0, 1], q 2 3 > 0 for u > 1+(q-1)(2–u)u

Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

Q: Evaluate the derivative of y = cos '2x - In 1-4x, where x = 0.125 -12> 2

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Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

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Q: Use the Chain Rule to express the second derivative off o gin terms of the first and second…

A: Let y=f o g then we have to find the second derivative of y.

Q: Find the derivative of f(x) = In(x² + 1) %3D

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Q: Q1 Prove that the derivative of (2x +1) 2 is 4 (2x + 1) by using first principle derivative.

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. x. 4 g(x)…

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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: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h(x)= […

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Q: Calculate the derivative 23 d dz using Part 2 of the Fundamental Theorem of Calculus. 23 dt = dz -1

A: ddx∫-1x6t5-t23dt = ?

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

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Q: In(5æ) Find the derivative with respect to x of y = %3D 5x y' = | %3D

A: Find the derivative

Q: 1.f(0) = (금x* + 3)" %3D

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h(x) = 2…

A: solution is given below

Q: Find the derivative of the function. (3x +5) f(x) = In (7x + 5)*(2x+ 8) 14 2 O a. 3x +5 + 7x +5 2x…

A: We have to check

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 1 dt = 1+ t2 f'(x) =

A: Given: f(x)=∫2x11+t2 dt By using part I of the Fundamental Theorem of calculus to find the…

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 25th derivative of g (0) = cos(40 + a) where a is a real valued constant.

A: The given function is: g(θ)=cos(4θ+α)

Q: Q1 Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

A: as per our guidelines we are supposed to answer only the first question. Kindly repost other…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the func - 2t dt g(x) =…

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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: 1. Find the directional derivative of the scalar function f = yzx^2 + 4xz^2 at the point P(1,-2,-1)…

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Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

A: To find the derivative of the h(x) using fundamental theorem of calculus part 1.

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…

A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…

Q: 3. Find the derivative of h()= 5²°-2z-1 %3D

A: We have to find derivative

Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: Solution :1.fx=23x3-2xfirst derivative ,f'xf'x=29x2-2Second derivative…

Q: Find the derivative, g' (x) for the function 1 t -dt 1+t3 g(x) = 3z+2 9z+6 1+(3z+2) (1+(3z+2)*)-…

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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: (d) Compute the driectional derivative of f at (1,2) in the direc- tion u = (e) • point (1, 2)? What…

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Q: 4. Show that the derivative of log,(Va +5) is 3(r + 5) In(2)

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 4 3 +2…

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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: 3. Find the derivative of (x² + 3) (3x – 3)² Y = Vrez+1 Hint: Use logarithmic differentiation!

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Q: Use the Derivative Rule in Section 3.8, Theorem 3, to derive d 1 sec dx x. 지 V - 1 1지 > 1.

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Q: Find the fourth derivative of f (z) = 3* + In (z) – 191z. Enclose arguments of functions in…

A: To find :  Fourth derivative of function ,  f(x)=3x+lnx-191x

Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: Find the fourth derivative of f (z) = 57 + In (z) – 109z. Enclose arguments of functions in…

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Q: 4. Compute the derivative of f(x) in each part. (a) f(x) = sin(ev) (b) f(x) = (tan r)", x € (0, 7/2)…

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Q: Find the fourth derivative of f (z) = 27 + In (z) – 160z. %3D

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Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: 2) Use the Chain Rule to express the second derivative of ƒ • g in terms of the first and second…

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Q: Compute the derivative of g(x) .3 = [ 1 dt- 1+ t5 3x2 1+ x15 1+ 25x 3x2 2" In 2 1+ x15 1+ 25a 23 1+…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. '6 G(x) :…

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Q: Find the derivative of the function. 8 f(x) =x" log 6x .7 ,7 O A. X +8x log ,x .7 O B. In 6 + 8x log…

A: According to product rule of differentiation ddxuv=vddxu+uddxv and according to power rule of…

Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

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Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

A: We have to find the required second derivative at the given point.

Q: Find the derivative using the First Fundamental Theorem of Calculus. 13)음 V8t +7 dt dx

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Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

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