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: (Implicit differentiation). Consider the curve 1/t + 1/s = 1 Find d/s = d/t Find d/t = d/s Show…

A: Given that: 1t+1s=1

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

A:

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…

Q: (b) u = Vt² + 2vt3 - 1 tan I (d) y = sec I VE-1 (f) y = VI+1

A: Since you have asked multiple subpart, as per our guidelines we are supposed to answer only first 3…

Q: Use the Fundamental Theorem of Calculus to find the derivative of 6 F(z) sin(t*)dt F'(r) = -sin(216)

A:

Q: Given 9 (x) = S* t² cos(t)dt use FTC Part 1 to compute g' (x).

A:

Q: Air is being pumped into a spherical weather balloon. Atany time t , the volume of the balloon is…

A: a) dV/dr means the rate of change of volume with respect to radius.  dV/dt means the rate of change…

Q: Find the derivative of y with respect to 0 y = 8e°(sin e - cos €) O 16e° sin e 8e (sin e - cos 0) +…

A: Given. We are given function of Y and theta and we need to find the function dY/d theta The concept…

Q: f'u where f(u) =ln(cos(g(2u)))

A: We have to find the derivative of given composition function

Q: (a) Let f(z) = sin*(z). Find f' (x), T(2) = (b) Let f(x) = J (x) = sin(z³). Find f'(x). %3D

A:

Q: 1 f(t) = (csc t- 1) %3D

A: Given derivative is as below:

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of » sin ( z ) h(2) = | .…

A: simply put at the place of sinx and multiply it by differentiation of sinx

Q: What is the first derivative of t(x) = arccsc(x4). Sorry, that's incorrect. Try again? t'(x) = 7 4 1…

A:

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

A:

Q: Find the derivative of the function. F(x) = dt F'(x) =

A:

Q: 45. y=- 17-3x z-1 z+1 46. x= (y-1) = (y +2y) 47. z

A: