1.

Find the first order partial derivatives of f(x,y)=y^5-3xy​

Answer»

ANSWER:

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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


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