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Hint
Solution
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Your problem, done right
One more of the same kind
Find the derivative of{{g.s}} {{g.s}}
Calculus I · Derivatives
The chain rule
How to differentiate a function that sits inside another function.
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Try another x:
x{{b.x}}
inside (u)3x + 1
inside (u){{b.u}}
outsideu2
f(x){{b.y}}
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Which is the inside?
Correct.
All six have the same shape: an outside acting on an inside.
The chain rule
Memorize this
Why does this work? (Optional)
- For a visual explanation, watch this video from the start to 1:48, then from 8:41 to the end.
- For an algebraic explanation, read the proof of the chain rule in Paul’s Online Math Notes.
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Find the mistake
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As an exam would set it
Work it on paper first, every step written out.
Model solution
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All three are there: the whole method, in the form an exam expects.
Your rules
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