Find the derivative of the function fx xx hint x eln x

Question

MATH 16A WORKSHEET 11-

There are 5 problems (one on the back).

(1) Find the derivative of the function f(x) = x^x. (Hint: x = e^{ln x})

(2) Use logarithmic differentiation to find the derivative of f(x) = (x - 2)³(-3x - 1)⁴/(x² - 2)⁵.

(3) Find f''(t) where f(t) = (ln t)².

(4) Let f(x) = ae^x2-3x + b(x + 1)². Find a and b if f(x) contains the point (0, 26) and the tangent line to f at this point has slope 17.

(5) Find all absolute minima and absolute maxima of the function

f(x) = x/x + ln x, defined on (1, ∞).