Question

Derivada da função y = e^(xlnx) ????

Answer 1

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$\sf y=e^{x\ell n(x)}\\\sf \dfrac{dy}{dx}=e^{x\ell n(x)}\cdot\bigg(\ell n(x)+\diagdown\!\!\!x\cdot\dfrac{1}{\diagdown\!\!\!x}\bigg)\\\sf \dfrac{dy}{dx}=e^{x\ell n(x)}\cdot(\ell n(x)+1)\\\sf mas~e^{x\ell n(x)}=x^x~DA\acute I:\\\huge\boxed{\boxed{\boxed{\boxed{\sf\dfrac{dy}{dx}=x^x\cdot(\ell n(x)+1)}}}}\blue{\checkmark}$