How do you find the derivative of ${log x}^{2}$ $logx^2$ ?

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How do you find the derivative of ${log x}^{2}$ $logx^2$ ?

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Answer 1 · 2016-01-10T00:40:22

$\frac{2}{x ln 10}$ $2/(xln10)$

Explanation:

Use logarithm rules to rewrite the function as

$2 log x$ $2logx$

Also, recall that $log x = {log}_{10} x$ $logx=log_10x$ , and apply the change of base formula to the logarithm to put it into a form containing the natural logarithm.

$2 (\frac{ln x}{ln 10})$ $2(lnx/ln10)$

If we want to differentiate this, remove the core function, $ln x$ $lnx$ , from the constant it's being multiplied by.

$\frac{2}{ln 10} \cdot ln x$ $2/ln10*lnx$

Finding the derivative:

$\frac{2}{ln 10} \cdot \frac{d}{d x} [ln x]$ $2/ln10*d/dx[lnx]$

$\frac{2}{ln 10} \cdot \frac{1}{x}$ $2/ln10*1/x$

$\frac{2}{x ln 10}$ $2/(xln10)$

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How do you find the derivative of ${log x}^{2}$ $logx^2$ ?

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Explanation:

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How do you find the derivative of ${log x}^{2}$ $logx^2$ ?