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Science
:
Math Exam Resources/Courses/MATH100/December 2010/Question 01 (c)/Solution 1
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From UBC Wiki
<
Science:Math Exam Resources
|
Courses/MATH100
|
December 2010
|
Question 01 (c)
Using the Product Rule, we get:
f
′
(
x
)
=
(
x
cos
x
)
′
=
(
x
)
′
(
cos
x
)
+
x
(
cos
x
)
′
=
cos
x
+
x
(
−
sin
x
)
=
cos
x
−
x
sin
x
{\displaystyle \displaystyle {\begin{aligned}f'(x)&=(x\cos {x})'\\&=(x)'(\cos {x})+x(\cos {x})'\\&=\cos {x}+x(-\sin {x})\\&=\cos {x}-x\sin {x}\end{aligned}}}