1. Find the derivatives of the following functions.

(a) \( \displaystyle f(x)= \ln{(\sec{x})} \)


Solution


(b) \( \displaystyle f(x)= \tan{(\ln{x})} \)


Solution


(c) \( \displaystyle f(x)= \ln{(x\cot{x})} \)


Solution


(d) \( \displaystyle f(x)= \log_5(x^3-2\sqrt{x}) \)


Solution


2. Find an equation of the tangent line to the curve \( y=2x\ln(x) \) at the point \((e, 2e) \).


Solution


3.Use logarithmic differentiation to find the derivative of the function \( y= (\sec{x})^{\sqrt{x}} \).


Solution