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Please find derivation of the following equation.

  • Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.
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$\large f(x)=e^{x^{2}}\ln x$

$\large f'(x)=e^{x^{2}}\frac{\mathrm{d} }{\mathrm{d} x}\ln x+\ln x \frac{\mathrm{d} }{\mathrm{d} x}e^{x^{2}}$

$\large f'(x)=e^{x^{2}}\frac{1}{x}+\ln x e^{x^{2}}\frac{\mathrm{d} }{\mathrm{d} x}x^{2}$

$\large f'(x)=e^{x^{2}}\frac{1}{x}+\ln x e^{x^{2}}(2x)$

$\large f'(x)=e^{x^{2}}(\frac{1}{x}+2x\ln x)$
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