What is the derivative of $f (x) = \sqrt{1 + {log}_{3} (x)}$ $f(x)=sqrt(1+log_3(x)$ ?

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Answer 1 · 2018-03-15T17:56:11

$\frac{d}{d x} (\sqrt{1 + {log}_{3} x})$ $d/dx(sqrt(1+log_3x))$

$= \frac{(\frac{d}{d x}) (1 + {log}_{3} x)}{2 \sqrt{1 + {log}_{3} x}}$ $=((d/dx)(1+log_3x))/{2sqrt(1+log_3x)}$

$= \frac{(\frac{d}{d x}) (1 + \frac{log x}{log 3})}{2 \sqrt{1 + {log}_{3} x}}$ $=((d/dx)(1+logx/log3))/{2sqrt(1+log_3x)}$

$= \frac{\frac{1}{x ln 3}}{2 \sqrt{1 + {log}_{3} x}}$ $=(1/(xln3))/{2sqrt(1+log_3x)}$

$= \frac{1}{2 x ln 3 \sqrt{1 + {log}_{3}}}$ $=1/(2xln3sqrt(1+log_3))$

What is the derivative of f(x)=sqrt(1+log_3(x)f(x)=√1+log3(x)f(x)=sqrt(1+log_3(x) ?