Find dy/dx if x siny+x cube y square=tan inverse y
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1
Answer:
We expand using the formula
cos
(
A
+
B
)
=
cos
A
cos
B
−
sin
A
sin
B
.
y
=
cos
x
cos
y
−
sin
x
sin
y
d
d
x
(
y
)
=
d
d
x
(
cos
x
cos
y
−
sin
x
sin
y
)
d
d
x
(
y
)
=
d
d
x
(
cos
x
cos
y
)
−
d
d
x
(
sin
x
sin
y
)
Remember that we are differentiating with respect to
x
here.
1
(
d
y
d
x
)
=
−
sin
x
(
cos
y
)
−
sin
y
(
d
y
d
x
)
(
cos
x
)
−
(
cos
x
(
sin
y
)
+
cos
y
(
sin
x
)
d
y
d
x
)
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