if f(x)=log⁡ex3−x3+x1/3 then f '(1) is equal to

f(x)=log⁡ex3−x3+x1/3=x+13[log⁡(3−x)−log⁡(3+x)]f′(x)=7−x29−x2f′(1)=7−19−1=68=34

if f(x)=log⁡ex3−x3+x1/3 then f '(1) is equal to

f(x)=log⁡ex3−x3+x1/3=x+13[log⁡(3−x)−log⁡(3+x)]f′(x)=7−x29−x2f′(1)=7−19−1=68=34

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if $f (x) = \log [e^{x} {(\frac{3 - x}{3 + x})}^{1 / 3}]$ then f '(1) is equal to

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Detailed Solution

$f (x) = \log [e^{x} {(\frac{3 - x}{3 + x})}^{1 / 3}]$
$\begin{array}{l} = x + \frac{1}{3} [\log (3 - x) - \log (3 + x)] \\ f^{'} (x) = \frac{7 - x^{2}}{9 - x^{2}} \\ f^{'} (1) = \frac{7 - 1}{9 - 1} = \frac{6}{8} = \frac{3}{4} \end{array}$

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