6. Derivatives of Inverse, Exponential, & Logarithmic Functions

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

y = (x^2 - 2x + 2)e^(x)

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

y = e^(θ)(sinθ + cosθ)

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

y = cos(e^(-θ^2))

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

y = ln(3te^(-t))

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

y = ln(e^(θ)/(1+e^θ))

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

y = e^(cost+lnt)

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

5. y = ln(sin²θ)

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

19. y = (sech θ)(1-ln(sech θ))

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

21. y = ln(cosh v) - 1/2 tanh²v

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

13. y = 6sinh(x/3)

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

15. y = 2√t tanh(√t)

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

17. y = ln(sinh z)

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

23. y = (x²+1)sech(ln x)

(Hint: Before differentiating, express in terms of exponentials and simplify.)

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

1. y = 10e^(-x/5)

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

3. y = (1/4)xe^(4x) - (1/16)e^(4x)