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. displaystyle f{{left({x}right)}}={e}^{{frac{{x}^{2}}{{{x}^{3}+{2}}}}}

Question
Derivatives
asked 2021-01-06
Find derivatives of the functions defined as follows. \(\displaystyle f{{\left({x}\right)}}={e}^{{\frac{{x}^{2}}{{{x}^{3}+{2}}}}}\)

Answers (1)

2021-01-07
\({f}'{\left({x}\right)}={e}^{{\frac{{x}^{2}}{{{x}^{3}+{2}}}}}{\left(\frac{{{\left({x}^{3}+{2}\right)}{\left({2}{x}\right)}-{x}^{2}{\left({3}{x}^{2}\right)}}}{{{\left({x}^{3}+{2}\right)}^{2}}}\right)}\)
\(={e}^{{\frac{{x}^{2}}{{{x}^{3}+{2}}}}}{\left(\frac{{{4}{x}-{x}^{4}}}{{{\left({x}^{3}+{2}\right)}^{2}}}\right)}\)
0

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