Samuel, a county social worker, helps county residents who are struggling with different issues. He uses “c” to indicate client
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If
then by the product rule,
and by the chain rule,
which leaves us with
Alternatively, if you exclusively want to use the chain rule, you can carry out logarithmic differentiation:
By the chain rule, differentiating both sides with respect to <em>x</em> gives
Solve for <em>f'(x)</em> yields
just as before.