// Numbas version: finer_feedback_settings {"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": "

$y=\\var{c[0]}\\sin(x)$

$\\frac{dy}{dx}=$ [[0]]

Ejemplo de respuesta: si la respuesta es $-2\\sin{2x}$, digite -2sin(2x) en la barra de respuesta.

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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 $f(x)=\\sin(x)$

Reglas de derivada que hay que aplicar:
$\\dfrac{d}{dx}[kf(x)]=kf'(x)$
$\\dfrac{d}{dx}[\\sin{x}]=\\cos{x}$
$\\dfrac{d}{dx}[\\cos{x}]=-\\sin{x}$
$\\dfrac{d}{dx}[\\tan{x}]=\\sec^2{x}$
$\\dfrac{d}{dx}[\\cot{x}]=-\\csc^2{x}$
$\\dfrac{d}{dx}[\\sec{x}]=\\sec{x}\\tan{x}$
$\\dfrac{d}{dx}[\\csc{x}]=-\\csc{x}\\cot{x}$

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$y=\\var{d[0]}\\cos(x)$

$\\frac{dy}{dx}=$ [[0]]

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$y=\\var{c[2]}\\tan(x)$

$\\frac{dy}{dx}=$ [[0]]

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$y=-\\sin(x)+\\var{d[2]}x^2$

$\\frac{dy}{dx}=$ [[0]]

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Reglas de derivada que hay que aplicar:
$\\dfrac{d}{dx}[kf(x)]=kf'(x)$

$\\dfrac{d}{dx}[x^n]=nx^{n-1}$
$\\dfrac{d}{dx}[f+g]=f'+g'$

$\\dfrac{d}{dx}[\\sin{x}]=\\cos{x}$
$\\dfrac{d}{dx}[\\cos{x}]=-\\sin{x}$
$\\dfrac{d}{dx}[\\tan{x}]=\\sec^2{x}$
$\\dfrac{d}{dx}[\\cot{x}]=-\\csc^2{x}$
$\\dfrac{d}{dx}[\\sec{x}]=\\sec{x}\\tan{x}$
$\\dfrac{d}{dx}[\\csc{x}]=-\\csc{x}\\cot{x}$

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$y=\\var{d[1]}\\sin(x)-(\\var{c[1]}\\cos(x))$

$\\frac{dy}{dx}=$ [[0]]

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Calcular la derivada de las siguientes funciones.

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extra coeff's added

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Differentiation of trigonometric functions

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