Differentiate the following functions with respect to x :

1.	Differentiate the following functions with respect to x :
Answer» $\rule{320}4$ ⠀ $\huge\tt\underline{QUESTION}\::$ ⠀ Differentiate the FOLLOWING FUNCTIONS with RESPECT to X : $\Large\sf\frac{x\:+\:e^x}{1\:+\:log_x}$ ⠀ $\rule{320}4$ ⠀ $\huge\tt\underline{SOLUTION}\::$ ⠀ $\sf {\huge\dashrightarrow}{\large \:\:\:\:\:y \:=\: {\Large\frac{x\:+\:e^x}{1\:+\:log_x}}}$ ⠀ $\sf {\Large\dashrightarrow}{\large\:\:\:\:\: \frac{d_y}{d_x}\:=\:\frac{ (1+log_x)\:\frac{d}{d_x}\:(x+e^x)\:-\:(x+e^x)\:\frac{d}{d_x}\:(1+log_x) }{(1+log_x)^2 }}$ ⠀ $\sf {\Large\dashrightarrow} {\large \:\:\:\:\:\frac{d_y}{d_x}\:=\:\frac{ (1+log_x)\:(1+e^x)\:-\:(x+e^x)\:(\frac{1}{x}) }{(1+log_x)^2 }}$ ⠀ $\sf {\Large\dashrightarrow}{\large \:\:\:\:\:\frac{d_y}{d_x}\:=\:\frac{(1\:+\:e^x) }{(1\:+\:log_x)}\:-\:\frac{(x\:+\:e^x)}{x(1\:+\:log_x)^2}}$ ⠀ $\rule{320}4$

Answer»

$\rule{320}4$