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Question #118865
f(x) = √(cosx) + √(sinx) dx
Expert's answer
f
(
x
)
=
(
cos
x
)
+
(
sin
x
)
f(x)=\sqrt{(\cos x)}+\sqrt{(\sin x)}
f
(
x
)
=
(
cos
x
)
+
(
sin
x
)
d
f
d
x
=
1
2
(
cos
x
)
(
−
sin
x
)
+
1
2
(
sin
x
)
(
cos
x
)
=
{df\over dx}={1\over 2\sqrt{(\cos x)}}(-\sin x)+{1\over 2\sqrt{(\sin x)}}(\cos x)=
d
x
df
=
2
(
cos
x
)
1
(
−
sin
x
)
+
2
(
sin
x
)
1
(
cos
x
)
=
=
cos
x
2
(
sin
x
)
−
sin
x
2
(
cos
x
)
={\cos x\over 2\sqrt{(\sin x)}}-{\sin x\over 2\sqrt{(\cos x)}}
=
2
(
sin
x
)
cos
x
−
2
(
cos
x
)
sin
x
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#340153
on Dec 2023
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