// Numbas version: exam_results_page_options {"name": "CUATRO TRES Derivada FT", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["d", "c"], "name": "CUATRO TRES Derivada FT", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "
$y=\\var{c[0]}\\sin(x)$
\n$\\frac{dy}{dx}=$ [[0]]
\nEjemplo de respuesta: si la respuesta es
$-2\\sin{2x}$, digite -2sin(2x) en la barra de respuesta.
En este tipo de ejercicios se deben considerar las reglas para derivadas de las funciones trigonométricas, además entender que la función es un múltiplo constante de una función trigonometrica, es decir: $kf(x)$, con $k=\\var{c[0]}$ y $f(x)=\\sin(x)$
\nReglas de derivada que hay que aplicar:
$\\dfrac{d}{dx}[kf(x)]=kf'(x)$
$\\dfrac{d}{dx}[\\sin{x}]=\\cos{x}$
$\\dfrac{d}{dx}[\\cos{x}]=-\\sin{x}$
$\\dfrac{d}{dx}[\\tan{x}]=\\sec^2{x}$
$\\dfrac{d}{dx}[\\cot{x}]=-\\csc^2{x}$
$\\dfrac{d}{dx}[\\sec{x}]=\\sec{x}\\tan{x}$
$\\dfrac{d}{dx}[\\csc{x}]=-\\csc{x}\\cot{x}$
$y=\\var{d[0]}\\cos(x)$
\n$\\frac{dy}{dx}=$ [[0]]
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\n$\\frac{dy}{dx}=$ [[0]]
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\n$\\frac{dy}{dx}=$ [[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "En este tipo de ejercicios se deben considerar las reglas para derivadas de las funciones trigonométricas, además entender que la función es un múltiplo constante de una función trigonometrica, es decir: $kf(x)$
\nReglas de derivada que hay que aplicar:
$\\dfrac{d}{dx}[kf(x)]=kf'(x)$
$\\dfrac{d}{dx}[x^n]=nx^{n-1}$
$\\dfrac{d}{dx}[f+g]=f'+g'$
$\\dfrac{d}{dx}[\\sin{x}]=\\cos{x}$
$\\dfrac{d}{dx}[\\cos{x}]=-\\sin{x}$
$\\dfrac{d}{dx}[\\tan{x}]=\\sec^2{x}$
$\\dfrac{d}{dx}[\\cot{x}]=-\\csc^2{x}$
$\\dfrac{d}{dx}[\\sec{x}]=\\sec{x}\\tan{x}$
$\\dfrac{d}{dx}[\\csc{x}]=-\\csc{x}\\cot{x}$
$y=\\var{d[1]}\\sin(x)-(\\var{c[1]}\\cos(x))$
\n$\\frac{dy}{dx}=$ [[0]]
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"}, "d": {"definition": "repeat(random(2..9),8)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "Differentiation of trigonometric functions
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}]}], "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}