6. Derivatives of Inverse, Exponential, & Logarithmic Functions

22–36. Derivatives Find the derivatives of the following functions.

f(x) = tanh²x

Find the derivative of the given function.

$g(x)=e^{x^2\(\ln\) x}$

Find the derivative of the given function.

$h\(\left\)(x\(\right\))=\(\sin\]\left\)(\(\log\)_4\(\left\)(x^2\(\right\))\(\right\))$

7–28. Derivatives Evaluate the following derivatives.

d/dx ((ln 2x)⁻⁵)

22–36. Derivatives Find the derivatives of the following functions.

f(x) = ln sech x

Find the derivative of the given function.

$f(x)=-3e^x+5x-2$

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))

Find the derivative of the given function.

$y=x^2e^{3x^2+5x}$

22–36. Derivatives Find the derivatives of the following functions.

f(x) = csch⁻¹(2/x)

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

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

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

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

Evaluate and simplify y'.

y = ln w / w⁵

7–28. Derivatives Evaluate the following derivatives.

d/dx (x^{π})

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

9. y = 8^(-t)