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If you have trouble with this question, please refer back to 'Differentiation 11 - Product Rule (Basic)' and/or 'Differentiation 9 - Chain Rule' and make sure you understand fully everything presented to you in the advice section.
\nYou should then be able to see how to apply the rules to the above questions.
", "rulesets": {}, "parts": [{"variableReplacements": [], "prompt": "$\\simplify{x^2(x+{c[0]})^{p[0]}}$
", "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "2x*(x+{c[0]})^{p[0]}+{p[0]}x^2*(x+{c[0]})^({p[0]}-1)", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "$\\simplify{{c[1]}x^3({c[2]}x+{c[3]})^{p[1]}}$
", "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "3{c[1]}x^2*({c[2]}x+{c[3]})^{p[1]}+{p[1]}{c[2]}{c[1]}x^3*({c[2]}x+{c[3]})^({p[1]}-1)", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "$\\simplify{{c[4]}x^{p[2]}({c[5]}x^2+{c[6]})^{p[3]}}$
", "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{p[2]}{c[4]}x^({p[2]}-1)*({c[5]}x^2+{c[6]})^{p[3]}+2{p[3]}{c[4]}{c[5]}x^({p[2]}+1)*({c[5]}x^2+{c[6]})^({p[3]}-1)", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "$\\simplify{(x+{c[7]})^{p[4]}(x+{c[8]})^{p[5]}}$
", "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{p[4]}(x+{c[7]})^({p[4]}-1)*(x+{c[8]})^{p[5]}+{p[5]}(x+{c[8]})^({p[5]}-1)*(x+{c[7]})^{p[4]}", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "$\\simplify{({c[9]}x^2+{c[10]})^{p[6]}({c[11]}x^2+{c[12]})^{p[7]}}$
", "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "2{p[6]}{c[9]}x*({c[9]}x^2+{c[10]})^({p[6]}-1)*({c[11]}x^2+{c[12]})^{p[7]}+2{p[7]}{c[11]}x*({c[11]}x^2+{c[12]})^({p[7]}-1)*({c[9]}x^2+{c[10]})^{p[6]}", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "statement": "Differentiate the following expressions with respect to $x$ using the product rule.
\nSimplify your answers as much as possible.
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