Suppose 8 (x) =Vx+1,What is the correct result of the second derivative of g with respect to x? %3D A8 (x) =- (x²+1)² 8"(x) = - *Vx²+1 (12+1)2 © 8(x)= - (x²+ 1)2 8"(x) =. x2+1 %3D

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: 3x-4 1. y = Arctan

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Q: Find the derivative of f(x) = (6x² + 6x – 4)arctan x 12x+6 бх2+бх-4 1 (6x2 + 6x – 4)aretan x…

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Q: Shows the derivative function of: 2x² + ln x²(2x² + 5x − 1)

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Q: 17) Find the first derivative of f(x) = (cos4x)6 6 or f(x) = cos 4x

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Q: 5. Find the first derivative of y = (2x³ – 1)5Vx² – 1 %3D

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Q: what would be the output if the 2nd derivative is negative

A: We know that for a function y = f(x), the points of extremum are obtained if the first derivative of…

Q: What is the first derivative of q(x) = In (4x² + 3x+2)? Select the correct answer below: In (8z + 3)…

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Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

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Q: Find the derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: Show that the derivative of the function sinh -¹ x can also be obtained by letting y = sinh -¹ x and…

A: Soln:To find the derivative of sinh-1x

Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: 2.) Investigate the derivate of the function ƒ(2)=Imz by using definiton of derivative.

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Q: 4. Find the 2nd derivative of f(x)=14-x (x)%3D

A: The give function is fx=4-x

Q: Obtain the second derivative of the function f(x) = 6 In(8x) – 3z4 and state the value of this…

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

A: Use rules of derivative

Q: y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y…

A: d2dx2arctan3x-44=d2dx2arctan3x-42=ddx1x3x-4=-9x-82x23x-43x-4…

Q: find the derivativey=log(to the 4th) time (2x Third -6x)

A: To apply the rules for derivative of composite functions

Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

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Q: Find the first derivative: y = In V2r³ – 5 O y =: 22-5 O y = 4z 22-5 O y = 62 22-5 O y =; 2z-5 O y =…

A: Here we have to find the first derivative of         y = ln(2x3-5)1/3

Q: Determine the derivative of y = ln(4x² - 2x). O 8x-2 4x-1 8x-2 4x²-x 4x-1 4x²-x 4x-1 2x2- -x O O

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Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Choose the derivative of sin (x). - 1 1 1+ x2 1 x2 | 1 1+ x2 1 xVx2 1 - 1 V1- x?

A: It can easily find the derivative of function

Q: 2 Find the derivative of: 9/x + 4x – 2 - - d 2 + 4x - - dx II

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Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: The first derivative of y = sin( 4x + 3) is %3D а. - 4 cos(4x +3) b. 4 cos(4x +3) С. cos(4x+3) d. -…

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Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

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Q: Find the derivative of xn by first principle or ab-initio method.

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Q: Approximate the derivative of f(x) = x² + 4x + 5 at x = 3 using the forward, backward, and central…

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: 1. 8rd Derivative of fC x) = 4 x³ - 8x5 1

A: We will use just the basic knowledge of differential calculus to answer this question step-wise.

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFF (x) = Vx + 2.

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Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: Find the derivative of f(x) = 9 sinh-' (x²) – 9 In ( Vx4 + 1). %3D

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Q: Find the derivative of y = csc(V3x² +1

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

A: We have to find derivative

Q: In 5 Find the derivative of y = logs ()) with respect to independent variablex.

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Q: Find the derivative of the following using General Rule. 7) y = vt3 8) f(x) = 6 + 5 1 9) y =-+ 2 x3…

A: We have to find derivative of Given function.

Q: 2. Determine the second derivative of f (x)=xe* at x = -2 with a step-size of h=0.50 using Central…

A: Given f(x) = x2e2x

Q: In(X+ bnx) %3D

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Q: Find a function with the given derivative whose graph passes through point P f'(x)=1/x+2, x is…

A: The derivative is given as

Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

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: Suppose we are asked to compute the 100th derivative of x 3 . How can we obtain the answer in a fast…

A: Solve the following

Q: Find the derivative of f (x) = In(3x² – x)³ in two different ways; (a) with the chain rule %3D | and…

A: Given fx=ln3x2−x3aUsing Chain Rulelnfx'=1fxf'xDifferentiate w.r.t…

Q: Find the derivative of f(x) = arctan x In(6x² + 6x – 4) 1 1 arctan x 6x2+6x-4

A: Here the given function fx=tan-1x ln6x2+6x-4

Q: 1.Find the derivative of y = - arcsin %3D V4-x2

A: Given:        y=x4-x2-arcsinx2 differentiating on both sides     dydx=ddxx4-x2-arcsinx2…