Algebraic derivative Problems and solutions

The algebraic functions are involved in differentiation. So, it is essential to learn the derivative rules of algebraic functions firstly to know how to use them as formulas in finding the derivatives of the algebraic functions. The following questions are the list of derivative problems with solutions in different methods to learn how to evaluate the derivatives of the algebraic functions in differential calculus.

Evaluate $\dfrac{dy}{dx}$ if $y \,=\, e^{\displaystyle \, x+3\log_{e}{(x)}}$