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

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

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

Relevant Questions

Find derivatives of the functions defined as follows: $$\displaystyle{y}={x}^{{{e}{x}}}$$
Use the rules for derivatives to find the derivative of function defined as follows.
$$\displaystyle{q}={\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{4}}}$$

Find derivatives of the functions defined as follows. $$y=3 \cdot 4^{x^{2}+2}$$

Find derivatives of the functions defined as follows. $$y=(te^{t}=2)/(e^{2t}+1)$$

Calculate the derivatives of the functions. Then find the values of the derivatives as specified.
$$\displaystyle{f{{\left({x}\right)}}}={4}-{x}^{{{2}}};{f}'{\left(-{3}\right)},{f}'{\left({0}\right)},{f}'{\left({1}\right)}$$
Use the rules for derivatives to find the derivative of each function defined as follows. $$\displaystyle{y}={2}{\tan{{5}}}{x}$$
consider the product of 3 functions $$\displaystyle{w}={f}\times{g}\times{h}$$. Find an expression for the derivative of the product in terms of the three given functions and their derivatives. (Remeber that the product of three numbers can be thought of as the product of two of them with the third
$$\displaystyle{w}'=$$?
$$\displaystyle{f{{\left({x},{y}\right)}}}={e}^{{{2}{x}{y}}}$$
$$\displaystyle{f{{\left({x},{y}\right)}}}={\frac{{{x}^{{{2}}}}}{{{x}^{{{2}}}+{y}^{{{2}}}}}}$$
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{\sin{{h}}}{x}}}{{{1}+{\sin{{h}}}{x}}}}$$