Practice Problem #23

Question

Suppose

(a) Find   . (Hint: Apply the laws of logarithms to  before taking its derivative.)

(b) Find  

Answer 1

a) Applying the rules of logarithms, we can expand f(x) to become f(x) = ln(e) + ln(x⁸) - ln(x - 3)⁶ = 1 + 8ln(x) - 6ln(x - 3)

So f'(x) = 8/x - 6/(x - 3)

b) The derivative of e^x = e^x so, applying the chain rule, the derivative of e^f(x) = e^f(x)•f '(x)