Question

derivada de x^2 . sen x . e^x

Answer 1

$\large\boxed{\begin{array}{l}\rm x^2\cdot sen(x)\cdot e^x\\\rm \ell ny=\ell n[ x^2\cdot sen(x)\cdot e^x]\\\rm \ell ny=\ell nx^2+\ell n[sen(x)]+\ell n[e^x]\\\rm \ell ny=2\ell n(x)+\ell n[sen(x)]+\ell n[e^x]\\\rm\dfrac{dy}{dx}\cdot\dfrac{1}{y}=\dfrac{2}{x}+\dfrac{1}{sen(x)}\cdot cos(x)+\dfrac{1}{\diagup\!\!\!\!\!e^x}\cdot \diagup\!\!\!\!\!e^x\\\\\rm\dfrac{dy}{dx}\cdot\dfrac{1}{y}=\dfrac{2}{x}+cot(x)+1\\\rm\dfrac{dy}{dx}=y\cdot\bigg[\dfrac{2}{x}+cot(x)+1\bigg]\end{array}}$

$\large\boxed{\begin{array}{l}\rm\dfrac{dy}{dx}=y\cdot\bigg[\dfrac{2}{x}+cot(x)+1\bigg]\\\\\rm\dfrac{dy}{dx}=x^2\cdot sen(x)\cdot e^x\bigg[\dfrac{2}{x}+cot(x)+1\bigg]\end{array}}$