Finding Derivative Values


In Exercises 67–72, find the value of (f ∘ g)' at the given value of x.


f(u) = 1 − (1/u), u = g(x) = (1 / (1 − x)), x = −1

In Exercises 9–18, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a function of x.

y = (4 − 3x)⁹

Find the derivatives of the functions in Exercises 19–40.

p = √(3 − t)

Find the derivatives of the functions in Exercises 19–40.

s = (4 / 3π)sin(3t) + (4 / 5π)cos(5t)

Find the derivatives of the functions in Exercises 19–40.

y = (5 − 2x)⁻³ + (1 / 8)(2 / x + 1)⁴

Given $z={\left(x-y\right)}^9$, where $x=s^{2}t$ and $y=s{t}^2$, use the chain rule to find the partial derivatives $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$.

Given $z={\left(x-y\right)}^7$, where $x=s^{2}t$ and $y=s{t}^2$, use the chain rule to find the partial derivatives $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$.

10–19. Derivatives Find the derivatives of the following functions.

f(x) = ln(3 sin² 4x)

Derivative of ln|x| Differentiate ln x, for x > 0, and differentiate ln(−x), for x < 0, to conclude that d/dx (ln|x|) = 1/x