In Exercises 37-42, find f'(x) and state the domain of f'. 37. f(x) = In (x + 2) 38. f(x) = In (2x + 2)

Q: In Exercises 45–74, compute the derivative using derivative rules that have been introduced so far.

A: y=sinx2cosx2

Q: In Exercises 45–74, compute the derivative using derivative rules that have been introduced so far.

A: given: y=xcos(1-3x)

Q: 13. f (x) = sinx3 (2х-1)2

A: I have stated the used formulas in the solution

Q: Use mathematical induction to prove that the derivative of f (x) = xn equals nxn−1 whenever n is a…

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Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x

A: Given Data: Function: fx=x3+2xlnx The product rule of derivative is, ddxfx·gx=fxddxgx+gxddxfx Use…

Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

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Q: Choose the correct answer by using the Product rule of derivative. d dx - (x4.x7) is equal to…

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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: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

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Q: In Exercises 20–21, find a formula for the derivative using the power rule. Confirm it using…

A: NOTE: Refresh your page if you can't see any equations. . take derivative (using power rule)

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

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Q: 3. Calculate the derivative of f (x) = x2 +1 showing all your work.

A: Using the formula u by v = vd/DX(u)-u d/DX(v)/v^2 According to the bartleby guidelines I can  solve…

Q: In Exercises 45–74, compute the derivative using derivative rules that have been introduced so far.

A: Given that y=z+1z-1=z+1z-112

Q: S(x)= Jx-5

A: given that f(x)=1x-5 find the derivative from first principle f'x=limh→0 fx+h-fxh

Q: 2) Find the derivative of the function f(x) = (x³ – tan(4x² – 2)* |

A: Given :            To find the derivative of the given function                f(x) = x3 -…

Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

Q: Compute the derivative of f(x)= (ex2 +e-x2 )/(ex2 -e-x2 )

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Q: The tangent line to y = f(x) at (-1,-8) passes through the point (-7,5). Compute the following a.)…

A: The tangent line to y=f(x) at (-1,-8) passes through the point (-7,5)

Q: In exercises 9–14, find all critical numbers and use the Second Derivative Test to determine all…

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Q: In Exercises 67–73, estimate derivatives using the symmetric difference quotient (SDQ), defined as…

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Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

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Q: Solve for the derivative of the function using chain rule. 8. f(x)= sin (2x)cos (3x)

A: Given problem:- Solve for the derivative of the function using chain rule.   8.     f(x)= sin…

Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: Choose the correct value of derivative. d dx x+1 X () is equal to (Hint: Look at the note of section…

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Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

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Q: 13 Use the Linear Approximation to estimate Af for f(x): when a = 2 and Ax = 2+x %3D (Use decimal…

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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: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: Determine the local extrema for t(x) = -3x3 - N2 - 90x +1 using the First Derivative Test. %3D

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Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: By using first principle, show that the derivative of f(x)=- is x+1 1 S'(x) = (x+1)

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Q: 4. Find the maxima/minima of f(x) = x³ – x using both 1st and 2nd derivative test.

A: Consider the function: fx=13x3-x. Find maxima, minima.   Find f'x by applying axn'=anxn-1.…

Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

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Q: 2 12. f (x) = (1tsinx) Cosx

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

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