If
𝑧
=
sin
−
1
(
𝑥
3
+
𝑦
3
𝑥
−
𝑦
)
z=sin
−1
(
x−y
x
3
+y
3
), show that:
𝑥
2
∂
2
𝑧
∂
𝑥
2
+
2
𝑥
𝑦
∂
2
𝑧
∂
𝑥
∂
𝑦
+
𝑦
2
∂
2
𝑧
∂
𝑦
2
=
2
cos
3
𝑧
sin
𝑧
.
x
2
∂x
2
∂
2
z
+2xy
∂x∂y
∂
2
z
+y
2
∂y
2
∂
2
z
=2cos3zsinz.
Mathbot Says...
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