Question

Differentiate the following functions with respect to x : $\large\frac{x+e^x}{1+log_x}$
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Answer 1

$\rule{320}4$

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$\huge\tt\underline{QUESTION}\::$

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Differentiate the following functions with respect to x : $\Large\sf\frac{x\:+\:e^x}{1\:+\:log_x}$

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$\rule{320}4$

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$\huge\tt\underline{SOLUTION}\::$

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$\sf {\huge\dashrightarrow}{\large \:\:\:\:\:y \:=\: {\Large\frac{x\:+\:e^x}{1\:+\:log_x}}}$

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$\sf {\Large\dashrightarrow}{\large\:\:\:\:\: \frac{d_y}{d_x}\:=\:\frac{ (1+log_x)\:\frac{d}{d_x}\:(x+e^x)\:-\:(x+e^x)\:\frac{d}{d_x}\:(1+log_x) }{(1+log_x)^2 }}$

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$\sf {\Large\dashrightarrow} {\large \:\:\:\:\:\frac{d_y}{d_x}\:=\:\frac{ (1+log_x)\:(1+e^x)\:-\:(x+e^x)\:(\frac{1}{x}) }{(1+log_x)^2 }}$

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$\sf {\Large\dashrightarrow}{\large \:\:\:\:\:\frac{d_y}{d_x}\:=\:\frac{(1\:+\:e^x) }{(1\:+\:log_x)}\:-\:\frac{(x\:+\:e^x)}{x(1\:+\:log_x)^2}}$

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$\rule{320}4$