6. Derivatives of Inverse, Exponential, & Logarithmic Functions

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

8. y = ln kx, k constant

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

10. y = ln(t^(3/2))

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

12. y = ln(10/x)

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

14. y = ln(2θ+2)

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

16. y = (ln x)³

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

18. y = t√(ln t)

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

23. y = ln(x)/(1+ln(x))

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

25. y = ln(ln(x))

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

27. y = θ(sin(lnθ) + cos(lnθ))

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

29. y = ln(1/(x√(x+1)))

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

33. y = ln(sec(lnθ))

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

35. y = ln((x²+1)^5/√(1-x))

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = e^(-5x)

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = e^(5-7x)

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = xe^x-e^x