find the first order partial derivatives of f(x,y)=y^5-3xy
Answers
Answer:
so here is your answer with details
Step-by-step explanation:
Question:
Find the first-order partial derivatives of the given function.
f
(
x
,
y
)
=
y
5
−
3
x
y
Partial derivatives:
To evaluate partial derivative of a function
h
(
x
,
y
)
with respect to
x
, keep
y
as fixed number and evaluate derivative with respect to
x
. Similarly, to evaluate partial derivative of a function
h
(
x
,
y
)
with respect to
y
, keep
x
as fixed number and evaluate derivative with respect to
y
.
Answer and Explanation:
Given
The given function is
f
(
x
,
y
)
=
y
5
−
3
x
y
.
Solution
Partial differentiate the function
f
(
x
,
y
)
=
y
5
−
3
x
y
with respect to
x
.
∂
f
∂
x
=
∂
∂
x
[
y
5
−
3
x
y
]
=
−
3
y
Partial differentiate the function
f
(
x
,
y
)
=
y
5
−
3
x
y
with respect to
y
.
∂
f
∂
y
=
∂
∂
y
[
y
5
−
3
x
y
]
=
5
y
5
−
1
−
3
x
=
5
y
4
−
3
x
Therefore,
∂
f
∂
x
=
−
3
y
and
∂
f
∂
y
=
5
y
4
−
3
x