In Exercises 67–73, estimate derivatives using the symmetric difference quotient (SDQ), defined as the average of the difference quotients at h and -h: 1(f(a + h) – f(a) f (a – h) – f(a) -h f (a + h) – f(a – h) | 1 2h The SDQ usually gives a better approximation to the derivative than the difference quotient. 67. The vapor pressure of water at temperature T (in kelvins) is the atmospheric pressure P at which no net evaporation takes place. Use the following table to estimate P'(T) for T = 303, 313, 323, 333, 343 by computing the SDQ given by Eq. (1) with h = 10. т (К) 293 303 313 323 333 343 353 P (atm) 0.0278 0.0482 0.0808 0.1311 0.2067 0.3173 0.4754

Q: 41. What is the derivative of f(x) = secx + 3 csc x? A. f¹(x) = sec xtanx + 3cscx cotx 3cscx tanx C.…

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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: Use the definition of the derivative to find the equations of the lines described in Exercises…

A: We can use the definition of derivatives to find the equation of tangent line at any point on curve…

Q: In Exercises 13–24, compute the derivative using derivative rules that have been introduced so far.

A: We will use the power rule first and then use the chain rule   y=(x2+9x)-2 y'=-2(x2+9x)-3ddx(x2+9x)…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = dt…

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Q: Can you help with this question step by step please

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Q: In Exercises 13–24, compute the derivative using derivative rules that have been introduced so far.

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the fund h(x) = V5 +r3…

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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: In Exercises 173–176, use theresult of Exercise 172 to find the derivative of the function. h(x)=|x|…

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Q: 2.Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function: g(x) =…

A: Given data: The expression for the give function is gx=∫0x1t3+1dt. The derivative of the given…

Q: Use the quotient rule to find the derivative. 2.1 +6 f(x) = x2.0 + 1 2.6 3.7 +2.1x x1.1 - 15.6x 1.6…

A: You need to just apply quotient rule.

Q: Find the derivatives of all orders of the functions in Exercises

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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: In Exercises 13–24, compute the derivative using derivative rules that have been introduced so far.

A: Given: y=cos9θ+41 we know that ddxcoskx+c=-ksinkx+c where, c is constant

Q: Find the derivatives of the functions in Exercises 27. y = x2sin^2 (2x2)           28. y = x^-2sin^2…

A: To find derivative of 1) y=x2sin2(2x2)2y=x-2sin2(x3)

Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

A: Fundamental Theorem of Calculus: If f(x) is continuous over an interval [a,b] and the function h(x)…

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f (x) = 20 – Pdt .

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Q: Determine whether the following statement is true or false, and explain why. The chain rule is used…

A: Given: The chain rule is used to take the derivative of a product of functions.

Q: Find the first and second derivatives of the functions in Exercises 33-38. 1? + 5t – 1 - 34. s =

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

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Q: (*) 5

A: We know that derivative of xn is nxn-1. Here We use fundamental theorem of calculus then find g'(x).…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. (t - g'(s)…

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Q: Let f'(x) = 100x(2x+3)(x-5), use the first derivative test to determine the location of the local…

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Q: 4 3. Лх) — Зх - 5 %3D

A: Given that  f(x)=4/(3x-5)^2  To find the derivative of f(x)

Q: Exercise 1: Compute the derivative of the given function and find the slope of the line that is…

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Q: Find the derivative of f (x) = coth³(1In(x³)). %3D A 9x²coth?( In(x³)) csch2(In(x³)) - 9coth (…

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Q: Use the ħndanental Theorem Ot calculus part I to find the derivative Of hx)=

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of te function.

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Q: the function f(x) = In 5x +3x + 13). 6. Differentiate ° 7. Find the derivative of the function .2 y…

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Q: In Exercises 13–24, compute the derivative using derivative rules that have been introduced so far.

A: We have to find the derivative of y=7x-3

Q: Find the derivative of the given functions using chain rule. 1. f(x) = (2x + 1) 2. f(x) = (x² + 4x –…

A: To solve the following derivatives using chain rule and product as well as quotient rule.

Q: In Exercises 7–12, use the Quotient Rule to calculate the derivative.

A: Given:w=z2z+zdwdzz=9 =?