Approximate V126 using Ay f'(x) · Ax

Q: Find the derivative of h(x) = | 14 arctan(t) dt. h'(x) = ||

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Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

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Q: Compute dy/dx using the limit definition of the first derivative for f(x) = 3x2

A: Given function is f(x)=3x2. we have to find the derivative using limit definition .

Q: Find y" by implicit differentiation Va + Vy= 4

A: To  Determine: find the implicit differentiation Given: we have x+y=4 Explanation: we have x+y=4 so…

Q: Find the derivative of y 16 In (In(6x)). (Use symbolic notation and fractions where needed.) dy dx…

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Q: 'the line tangent to the graph of y= In(3x) + 2x e at x=1 6 Jx-1 by using quotient rule. Vx +1 for…

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Q: Use differential to approximate the change in y=x3+x2 as x changes from 1 to 0,95.

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Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

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Q: Take a look at the derivative of the integral * S (6t2 – 5t + 2) dt. (6t² dr Evaluate the…

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Q: Defermine the derivative of the following functions using the long method (using limits). 1. y =t –…

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Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: Use the derivative to find the critical point of f(x) = Ax² + Bx + C. Assume that A, B, and C are…

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Q: Find the general anti-derivative of f(x) = + Vx on a continuous interval.

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Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: Use forward and backward difference formula with h = 0.1 to approximate the derivative of f(x) =…

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

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Q: If f(x,y) = y2 ex + 3 ln (xy), find fxyy (1,1). fxyy (1,1) = ?

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Q: Find dy/dx for f(x)=(Inx)x^2

A: Given:y=fx=lnxx2We need to find: dydx

Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

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Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

A: Note:- For this problem, you don't mention any particular method and anything about h. So, I'll try…

Q: Use the Quotient Rule to show that the Powers of x Rule appies to negative Integer powers. That s,…

A: The given function is fx=1xk   where k>0. Quotient rule says that ddxfg=gdfdx-fdgdxg2.

Q: what the derivative fxy er hin ction Sas)=x'tan)

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Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: Ay Find the derivative of the following using lim Ax-0 Ar %3D dx ala

A: Part (a) - y = 4x2-5x       ...........(1)Given that,dydx = limx→0 ∆y∆x We can write it as - dydx =…

Q: 3. Use the forward-difference formula to approximate the derivative of f (x)=sin(In x) at x, = 2.5…

A: The derivative of the function can be calculated using the difference method. The formula for the…

Q: find dy/dx by implicit differentiation for: f(x)=In (2x+1)^3/squareroof of x^2+1

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Q: Evaluate the implicit function by finding dy/dx of x³+3y=3xy

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Q: Find the derivative of the function. *sin(x) y = Jcos(x) In(6 + 3v) g'(x) =

A: use Lebniz's Rule:   d/dx ∫[a(x),b(x)] f(t) dt =f(b(x))b' - f(a(x))a' Here, a(x) = cos(x) b(x) =…

Q: f(x) = x*Inx

A: TO FIND 5th order derivative f(x) = x4 lnx FORMULA USED  BIPART PRODUCT RULE OF DIFFERENTIATION…

Q: Find dy by dx when  f(x) =2x²-x+5÷3x+2

A: The derivative of a function gives the rate of change of a function when an infinitesimal change is…

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: 1. Find the derivative of the function:F(x)= [ (Vt arctan t)dt .

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Q: Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step…

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Q: what is the derivative of hcx) at x =D0 where h lx) =2f(6)-2-VFIR) where %3D

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Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: What is the first derivative of s(x)=(7x)3x at x=4? Select the correct answer below:…

A: As s(x)=(7x)3x The function can be rewritten as:s(x)=x3x. 73xIts first derivative is given by the…

Q: The derivative of x at X = 1 is to I Frue or false 2

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

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Q: Q Find the derivative us ing the de fini tion 2. O fcx) Fcx) x+2X %3D

A: Derivative of the function using definition

Q: Find the derivative ofy. with respect to x if y=(Ix +5) (9x² +2x) %3D

A: Given that: y=(x+5)(9x2+2x)

Q: 2 e -8; x(0) = 1 dt

A: Solution is given below:

Q: Find the first derivative or f(x) of the following functions using the techniques of integration.

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Q: 4. Find the Linearization of f (x) sinx at a Provide your answer as L(x) =?

A: The given problem is to find the linearization of the given function at given point. Given…

Q: 5. Find by implicit differentiation for x + y = xy. dx

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

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