Question #edd42

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Question #edd42

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Answer 1 · 2017-07-01T16:24:58

$= e^{x} + \frac{3}{x ln (10)}$ $=e^x+3/(xln(10))$

Explanation:

The final answer depends on whether $log (x)$ $log(x)$ is to be interpreted as the ${log}_{10} (x)$ $log_10(x)$ or ${log}_{e} (x) = ln (x)$ $log_e(x)=ln(x)$ (the natural logarithm). Let's assume you meant the log base 10.

$\frac{d}{d x} (e^{x} + 3 {log}_{10} (x))$ $d/dx(e^x+3log_10(x))$

$= \frac{d}{d x} (e^{x}) + \frac{d}{d x} (3 {log}_{10} (x))$ $=d/dx(e^x)+d/dx(3log_10(x))$

$= e^{x} + 3 \frac{d}{d x} ({log}_{10} (x))$ $=e^x+3d/dx(log_10(x))$

Using the change of base formula

$= e^{x} + 3 \frac{d}{d x} (\frac{ln (x)}{ln (10)})$ $=e^x+3d/dx(ln(x)/ln(10))$

$= e^{x} + \frac{3}{ln (10)} \frac{d}{d x} (ln (x))$ $=e^x+3/ln(10)d/dx(ln(x))$

$= e^{x} + \frac{3}{ln (10)} (\frac{1}{x})$ $=e^x+3/ln(10)(1/x)$

$= e^{x} + \frac{3}{x ln (10)}$ $=e^x+3/(xln(10))$

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Question #edd42

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