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Mathematics
Mathematics
Problem
(a) State the rule for the derivative of the product of two differentiable functions. (b) Let
f
(
x
)
=
x
sin
x
f(x)=x\sin x
f
(
x
)
=
x
sin
x
. Find
f
′
(
x
)
f'(x)
f
′
(
x
)
, showing each step clearly. (c) Explain briefly why the derivative obtained in part (b) naturally contains two separate terms.
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