Use Leibniz's Rule to find the derivatives of the functions in Exercises 31–-38. sin x 32. f(x) = 31. f(x) = 1/x dt ip² cos x r2Vy sin 1² dt cy² e' 33. g(y) = 34. g(y) = Vy In Vi dt In t dt 35. y = 36. y = x/2 rezo cInx 37. y In t dt 38. y = sin e' dt

Q: 10. Find the first derivative of sin (y) + cos (x) = 1. cosx siny sinx a. y' b. y' %3D cosy C. y'…

A: We have to find the first derivative of sin(y)+cos(x)=1.To find the derivative we use chain rule of…

Q: %3D %3D y = In ( sinh 2z) Find the derivative of y with respect to z.

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Q: In Exercises priate variable. 21. y = cos (r) 23. y = sin-'V21 25. y = sec (2s + 1) find the…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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Q: Find the derivative of the function. y = e4 e -20 - 20 cos 50 O A. - 5603 e - 20 , sin 50 O B. 03 e…

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Q: 5. Consider the function f(r, y) = sin(x² + y²). (a) direction of (4,3). Find the derivative of f(r,…

A: The directional derivative is the rate at which the function changes at a point in the direction .…

Q: Find j Partial derivative

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: In Exercises 21–42, find the derivative of y with respect to the appro- priate variable. 21. y =…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Calculate the derivative 5¢6 23 dt dz using Part 2 of the Fundamental Theorem of Calculus. 5,6 23 dt…

A: step 1: recalling fundamental theorem of calculus Step 2: interpreting with the given question step…

Q: In Exercises 13–18, find the derivative of y with respect to the appro-priate variable. 13. y = 6…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let f(x, y,z) = z-sin(xy), x = t, y = ln t , z = et-1 . Find derivative of f directly and by using…

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Q: Consider the differential equation I+y Using isoclines, construct a direction field, maybe even plot…

A: Given: y'=x-yx+y

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Q: Find general solutions of the differential equations . Primes denote derivatives with respect to x…

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Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i -3j b)…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. cOS X y =…

A: To use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.y=∫sin…

Q: Consider the differential equation where f and g are continuous functions.   (a) What type of…

A: To determine the type of equation obtained when the variable is changed using u = xy in the below…

Q: respect to x of/ /(3Vi-1) dt is 3x – 1 by the 2nd fundamental theorem of C The derivative with (A)…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 0. y = 3…

A: Given, y=∫ex03 sin2(t)dt  We need to calculate the value of y' It is of the form of…

Q: Calculate the derivative e12x d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus.…

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Q: In Exercises 25–36, find the derivative of y with respect to the appro- priate variable. 25. y =…

A: Hello thank you for the question. We’ll answer the first question since the exact one wasn’t…

Q: Use Theorem 12.33 to find the indicated derivatives in Exercises27–30. Express your answers as…

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Q: Differentiate the following functions with respect to X a) Y = e (3x + 2) b) Y = x² In x sin x c) Y…

A: As per guidelines we can solve three subparts at a time, so the first three subparts can be solved…

Q: Prove first that sinx siny dx - cosx cosy dy =0 is an exact differential equation then determine its…

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Q: Calculate the derivative d dz (2t5 34 dt using Part 2 of the Fundamental Theorem of Calculus.

A: The solution are next step

Q: L{t'sin(2t)}

A: I am attaching image so that you understand each and every step.

Q: Use Variation of Parameters to solve the differential equation. y"y tanx y C1cos xC2sin x - In secX+…

A: Result used:

Q: Consider the differential equation x²y" + xy' + y = 0; cos(In(x)), sin(In(x)), (0, 0). Verify that…

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Q: (a) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

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Q: cos(x² + y²) = y² sinx² y² = ln(x² + y²)

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

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Q: sint F(x) = √"* ( *ª*** ( √ ¹ + uª) du) dt Jo

A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

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Q: 14. Find the derivative of y = e cosz %3D A. y' = -ecosx sin z B. y' = elinx cos x C. y' = -etinx…

A: Given,y=ecosxdifferentiating both the sides w.r.t. xdydx=ddxecosxUsing chain…

Q: 2- Find the derivative of y with respect to the Exercises 1-3. y 1- 6 sinh || 1 y sinh (2x + 1) 2-…

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Q: Calculate the derivative d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus. Enclose…

A: Given that ,ddx ∫x3e5x   ln (t) dtTo apply fundamental theosem,ddx∫a(x)b(x) f(t) dt = f(b(x)). b1(x)…

Q: Determine whether the differential equation is exact. Show work to support your answer. sin(x) dy =…

A: The solution is given as

Q: Exercises: Find the first derivative of the functions: 1) y arcsin 4x %3D 2) x = arctan VE 3) 0 =…

A: Given The equation is y=x arcsin x  +1-x2 .

Q: Consider the differential equation du =U- U dt u – u°. the points of stability and plot the function…

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Q: 5. Using the method of stationary Phase find the leading term behavior of cos (xt*)dt as X 00.

A: To find the leading term behaviour of a function we need to analyze the asymptotic behaviour of the…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. tan x y =…

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Q: Exercise 3.1. Find the derivative of the following functions: y = tan 2x 2. g(x) = xsin x – 5 cos x…

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

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y = 2 sin3…

A: We can use fundamental theorem of calculus in order to solve the given problem.

Q: Use implicit differentiation with partial derivatives (as described in Example 4 page 732) to find…

A: Given function is, x2y+xy=4

Q: Calculate the derivative 25 dt dx using Part 2 of the Fundamental Theorem of Calculus. d dx 25 dt =

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Q: Find the derivative using the First Fundamental Theorem of Calculus. 13)음 V8t +7 dt dx

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Q: Calculate the derivative 33 4:6 dx using Part 2 of the Fundamental Theorem of Calculus. 33 dt = da

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Q: Use differential calculus to determine the exact position and nature of the stationary points for y…

A: We know that a stationary point of a function f(x) is a point where the derivative of y=f(x) is…

Q: Example2: Find the derivative of w=xy+z if x=cos t ,y=sin t &z=2t?

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