Find dy/dx for the following:
a. y = x^π
b. y = π^x
c. y = x^x
d. y = π^π
e. xy = π
a) very easy
b) dy/dx = (π^x) * ln(π)
c) tricky, first ln both sides
lny y = ln(x^x) = xlnx
y'/y = x(1/x) + lnx
y' = x^x (1 + lnx)
d) what is the derivative of a constant?
e) xy = π
x dy/dx + y = 0
dy/dx = -y/x