// Numbas version: exam_results_page_options {"name": "CINCO CUATRO Derivada producto", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "s2", "s1", "m", "n"], "name": "CINCO CUATRO Derivada producto", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "
Si $u$ y $v$ son funciones derivables de $x$, entonces
\\[\\simplify[std]{Diff(u * v,x,1) = u * Diff(v,x,1) + v * Diff(u,x,1)}\\]
Para en ejemplo se tiene que:
\n\\[\\simplify[std]{u = sin({a} + {b} * x)}\\Rightarrow \\simplify[std]{Diff(u,x,1) = {b} * cos({a} + {b} * x)}\\]
\n\\[\\simplify[std]{v = e ^ ({n} * x)} \\Rightarrow \\simplify[std]{Diff(v,x,1) = {n} * e ^ ({n} * x)}\\]
\nHaciendo la sustitución en la fórmula, se obtiene:
\n\\[\\begin{eqnarray*}\\frac{df}{dx} &=& \\simplify[std]{{b} * cos({a} + {b} * x) * e ^ ({n} * x) + {n} * sin({a} + {b} * x) * e ^ ({n} * x)}\\\\ &=&\\simplify[std]{({b}cos({a}+{b}x)+{n}sin({a}+{b}x))e^({n}x)} \\end{eqnarray*}\\]
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\n$\\displaystyle \\frac{df}{dx}=\\;$[[0]]
\nEjemplo de respuesta: digite 2cos(2+2x)e^(-5x)-5sin(2+2x)e^(-5x) en la barra de respuesta, para ingresar una solución de tipo:
$2\\cos(2+2x)e^{-5x}-5\\sin(2+2x)e^{-5x}$
Si $u$ y $v$ son funciones derivables de $x$, entonces
\\[\\simplify[std]{Diff(u * v,x,1) = u * Diff(v,x,1) + v * Diff(u,x,1)}\\]
Calcular la derivada de la función, empleano la regla del producto
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