6. Derivatives of Inverse, Exponential, & Logarithmic Functions

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

23. y=arcsin(√2t)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

25. y=arcsec(2s+1)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

27. y=arccsc(x²+1)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

29. y=arcsec(1/t), 0<t<1

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

31. y=arccot(√t)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

33. y=ln(arctan(x))

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

35. y=arccsc(e^t)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

37. y=s√(1-s²) + arccos(s)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

39. y=arctan√(x²-1) + arccsc(x), x>1

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

41. y= x arcsin(x) + √(1-x²)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

43. y=√(arcsin x)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

47. y=(arccot(x³))³

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

45. y=cos(x-arccos(x))

For problems 49–52 use implicit differentiation to find dy/dx at the given point P.

49. 3arctan(x) + arcsin(y) = π/4; P(1, -1)

For problems 49–52 use implicit differentiation to find dy/dx at the given point P.

51. y arccos(xy) = -3√2/4 π; P(1/2, -√2)