# Find derivatives of the functions defined as follows. displaystyle f{{left({x}right)}}={e}^{{frac{{x}^{2}}{{{x}^{3}+{2}}}}}

Find derivatives of the functions defined as follows. $f\left(x\right)={e}^{\frac{{x}^{2}}{{x}^{3}+2}}$
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${f}^{\prime }\left(x\right)={e}^{\frac{{x}^{2}}{{x}^{3}+2}}\left(\frac{\left({x}^{3}+2\right)\left(2x\right)-{x}^{2}\left(3{x}^{2}\right)}{{\left({x}^{3}+2\right)}^{2}}\right)$
$={e}^{\frac{{x}^{2}}{{x}^{3}+2}}\left(\frac{4x-{x}^{4}}{{\left({x}^{3}+2\right)}^{2}}\right)$