Evaluate the derivative of $f(x)=e^{\\cos x + 1}$ at the point $(\\pi,1)$.

", "advice": "", "rulesets": {}, "extensions": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "First, determine $f'(x)$:

\n$f'(x) = $ [[0]]

\nNow, evaluate the derivative at the point $(\\pi, 1)$:

\n$f'(\\pi)=$ [[1]]

", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n [\n [\"sin(x)*e^(cos(x)+1)\", \"Double check the rule for differentiating $\\\\cos x$.\"],\n [\"(cos(x)+1)*e^(cos(x))\", \"The power rule is only valid for a variable to the power of a number (e.g. $x^6$). Therefore, you cannot use the power rule for $e^{\\\\cos x + 1}$ (since the variable is in the power).\"],\n [\"e^(cos(x)+1)\", \"You're on the right track. The exponential function does not change when differentiated. However, when the power is more complicated than a single variable (e.g. $x$) on its own, what extra step do you need to perform?\"],\n [\"e^(-sin(x))\", \"Remember, the power on the exponential never changes when you differentiate it!\"],\n [\"e^(-sin(x)+1)\", \"Remember, the power on the exponential never changes when you differentiate it!\"],\n [\"-sin(x+1)*e^(cos(x+1))\", \"Be very careful when deciding what the argument of cosine is. The +1 is not part of the angle, as there are no brackets to group it with that $x$. The function is $e^{\\\\cos(x)+1}$.\"],\n [\"sin(x+1)*e^(cos(x+1))\", \"Be very careful when deciding what the argument of cosine is. The +1 is not part of the angle, as there are no brackets to group it with that $x$. The function is $e^{\\\\cos(x)+1}$. Also, double-check the rule for differentiating $\\\\cos x$.\"]\n ]\n\nparsed_malrules: \n map(\n [\"expr\":parse(x[0]),\"feedback\":x[1]],\n x,\n malrules\n )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n map(\n len(filter(not x ,x,map(\n try(\n resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n message,\n false\n ),\n vars,\n vset\n )))