22. Find the "natural" domain of the function f(x)=16r +Vx. x'-16x

Q: 0,-T <x<0 tsen x, 0sx < T 9. f(x) =

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Q: use definition to show that the function f(x)= |x|^3 is differentiable at 0, with derivative equal…

A: We have to use definition of differentiable:

Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

A:

Q: Find the derivative of the function f (x, y) = x²y + y²z: at Po(1,2,3) in the direction of û = 2î –…

A: To find the derivative of the function f(x,y)=x2y+y2z at P0(1,2,3) in the direction of…

Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

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 derivative of y with respect to x. 4. (x² - y²)² = 4ay²

A:

Q: Find the derivatives of the functions in Exercis

A: We have, f(x)=7+x sec x First, we write the above function in power form. fx=7+x sec x1/2

Q: B) Findfor the Implicit function: dx x² - sin(xy) + y² = 5xy

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Q: Find the derivative of the function. f(x) = (x³ + s ]Inx O a. x*(1+Inx)+5 O b. x'(1+31nx)+ 5 O c…

A: We have to check

Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

A:

Q: II. Obtain the required order or level of derivative. 1. y = 3x5 + 4x³ – 4x + 1, find y" 2. f(x)…

A: Solve differentiate

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: 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: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

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Q: Find the derivative of the function 3 f(x) = V (x² – 2)' at x = -1. f'(- 1) =

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Q: Find the derivative of the transcendental function. y' = y = 6e* x² +8 6(x²–2x+8)ex (x+8)²

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Q: Solve the first derivative of f(x) = 52x+1 at x = 0.5 using backward finite-divided difference and a…

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Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

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Q: 6. Determine the derivative of the function with respect to x. y = x2 – V2x +1

A: Solve the given problem.

Q: 5) Find the second derivative of f (x) = %3D ex plify your answer as much as possible

A: fx=1-2xexTo find the second derivative

Q: Find the derivative with respect to x of 1 f(x) V3x + 9

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Q: 4 Find the derivative of the function y= f(x)= Jx(x-8). %3D

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Q: Q2/ Find the derivative of the function f(x) = V3x +1 by definition %3D

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Q: A) Consider the function f(x) whose second derivative is f"(x)=4x+3sin(x). If f(0)=4 and f'(0)=4,…

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Q: 4. FIND d²y BY IMPLICIT DIFFERENTIATION: x² + y² = 81 %3D dx2

A: Given: x2+y2=81

Q: Consider the function f (x, y) = x²y³ – 3xy³. Compute the value of the derivative frvy at the point…

A: Given function is f(x,y) =  x2y3 - 3xy3 we have to find fxyy at the point (2,1).

Q: Compute the derivative function f'(x) algebraically. f(x) = 8x – 5 %3D f'(x) =

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

Q: B. By using the definition of the derivative, find the for: dx 1- f(x) = V %3D 2- f(x) = x -!

A:

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…

A:

Q: F(x)=In(52x+n • (x+2) ) %3D

A: Find the derivative of the function

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

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Q: Find the derivative of the function. 2 f(x) = 3F + 3cos x V X

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Q: Use the definition of the derivative to find: f(x)= 1/x^3 g(z)= z^4 - 8z^2

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: Find the derivative of the function f(x) = V (x² – 2)* at x = 1.

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

A:

Q: Q1) The dervative of the function f(x)= |x+2 using the definition of derivative is

A:

Q: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

A: Derivative of the function using definition

Q: 2. Find the derivative of (a) f(x) = x* + 4x 2 + 4e" (b) f(x) = 2 tan (x) – 6"

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Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=4f(0)=4 and…

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Q: Find the derivative of the function 4/ f f(x) = V (x – 3) at x = 2. f'(2) =

A: fx=x2-354⇒fx=x2-354 Differentiating with respect to x, we get f'x=ddxx2-354=54x2-354-1·dx2-3dx…

Q: 10 The derivative of the function f(x) = x7 + - 10 726 + (r³) 10 71° + (2) 1 10 7x + 10 10 726 (z²)…

A:

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: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

A:

Q: 4. The derivative of the function f(x) = r +3) is

A:

Q: Find the derivative of f(z)=((11z+4)1/2)(e3z).

A: Given function f(z)=11z+412e3z