Find the differential of each function.

Question

a) e ^ tan(pi*t)

b) sqrt (8+ln(z))

Answer 1

a. f(t) = e^[tan (pi *t)]
Let u = tan (pi t)
f(u) = e^u
df/dt = df/du du/dt
du/dt = pi * sec^2 (pi t)
df/du = e^u
df/dt = pi* e^[(tan (pi*t)]*sec^2 (pi*t)

b) Let u = 8 + ln z
f(z) = f[u(z)]) = sqrt u
Use the chain rule, as I did in (a)
df/dz = df/du*du/dz