// Numbas version: finer_feedback_settings {"name": "Chain Rule 1 (M)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Chain Rule 1 (M)", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "
Differentiate the following with respect to $x$:
\n\\[y=\\simplify{({a}x^{b}+{c})^{{d}}}\\]
", "advice": "Let $u(x)=x^{\\var{d}}$ and $v(x)=\\simplify{{a}x^{{b}}+{c}}$, then $y=u(v(x))$.
\nUsing the chain rule, we get
\n\\[\\dfrac{dy}{dx}= u'(v(x))\\times v'(x) = \\simplify{{d}({a}x^{b}+{c})^{{d}-1}}\\times \\simplify{{a}{b}x^{{b}-1}} = \\simplify{{d}x^{{b}-1}({a}x^{b}+{c})^{{d}-1}{a}{b}} \\]
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