Find the third Taylor's polynomial f(x) = x3 – x² + 3x + 1 which can easily find the derivative at xo = 0, x = 0.5 solution:

Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

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Q: Find y' by implicit differentiation 1. x³+y³=6xy 2. x²+y²=4

A: 1. Given: x3+y3=6xy To find y'by using implicit differentiation the implicit differentiation is…

Q: Find the differential of the function y=(3-x8)1/2

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Q: Find the differential quotient of the following functions: a) f(x)=5x–2 b) f(x)=x2 +3 c)…

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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: The derivative of the function y = tan(In(vx² – 6x + 1)) is: 2 -

A: Chain Rule : (fg(x))' = f'(g(x)).g'(x). d(ax+b)ndx = n.a(ax+b)n-1 dtanxdx = sec2(x)

Q: (a) Apply first principles, to calculate the differential coefficient of (x) = 5(3x²+2) when x = 3.

A: Solution a: Given function is f(x)=5(3x2+2) using first principle…

Q: 1 Find the derivative of f(x) = v2 – 3xª 2 -4 |

A: We use chain rule to find derivative

Q: Find the derivative of the following using First Principle. 4) y = -2x2 + 3x – 12 5) f(x) = x2 + 15x…

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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: (b) To determine To compute: The differential equaiton + x = sin 4t with initial condition x (1₁) =…

A: Given differential equation is: d2xdt2+x=sin4t . . . (1)The initial condition is: xt1=0 And…

Q: 2x+4 f(x) = (3x + 7) e.

A: Given query is to find the derivative of f(x).

Q: If u(x)= x²-1 and v(x)= x+1, find the first derivative of the product.

A: If u and v are two functions of x, then the derivative of the product uv is given by... d(uv)dx=…

Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: Find the third derivative of ƒ (z) = ¥9z +I. f" (2) =

A: Answer is mentioned below

Q: Find the 4th order differential of the function y=√2x+1.

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Q: Use partial differentiation to find the derivative of the implicit function dy (3x'y-1)+ 7xy = 9…

A: We will use the given formula to solve this question.

Q: Find the general solution of the differential equation with the help of lablace transform

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Q: 5. Use the properties of differential operators to solve for the product of (D+x²)(xD + 2)y

A: Given: D+x2xD+2y To find: Solution

Q: FIND THE SECOND DERIVATIVE OF THE FOLLOWING IN ITS SIMPLIFIED FORM. x = t/t-1 , y = t2/t2-1

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Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (2) — 5а — 4 %3D | 2. f…

A: Recall: Derivative using Four step Rule:step 1 : Write f(x+h) and f(x).step 2 : Compute f(x+h)-f(x)…

Q: S-2(x-1 - x²) dx 5.

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Q: 4. Find the derivative of the following by applying the chain Rule and simplify. a. f(x)=| x+3 b.…

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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: e3x-e-3x Y = e 3x+e-3x 4. t2 y= 72-1 5. X = t-1

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

A: We will solve the problem

Q: (b) Find the differential for y = -5 %3D

A: Giveny=4x-53   ...(1)

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

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Q: Find the differential of y² + x = 4.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: F(x)=In(52x+n • (x+2) ) %3D

A: Find the derivative of the function

Q: у %3D V1+ 2х (1 — х)-3

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Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

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Q: Find the derivative using the long method 3 u = t2

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Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

A: Equation is  f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…

Q: h(x) = In (2x-2)+(x² +1)e³x-6 %D Calculate the derivative at x=2, that is h'(2)=

A: calculate the derivative as shown below: h'x=ddxln2x-2+x2+1e3x-6…

Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

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: Find the derivative of y= (x³-1) /(x-1). O a. 2x -1 O b. 2x -3 O c. 2x + 3 O d. 2x + 1

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Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given, f(x)=sin(2x)+17

Q: Find the approximate root of y = 2x2 + 4x – 6 when x = 0.01 using differentials. -

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Q: Find the differential of the function. u = 3x4 + 4

A: The given function u=3x4+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 derivative of g(x) = J2x u²+1

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Q: Compute the derivative of x(x + 2) (2x + 1)(3x + 2) y = (a) directly using the Chain and Product…

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Q: Use the u-substitution to find the anti-derivative of h'(x)= xcos(2-3x2)

A: h'(x)=xcos(2-3x2) Formula ∫cos (x) dx= sin (x)+C

Q: Find a differential operator that annihilates the given function. xe3xsin5x

A: given function is                                                      f(x)=xe3xsin5x we have to…

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: Q1) Compute the derivative of the function f (t)= | sin² x²dx. -t

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