Question

1 If f(x, y) = x3 + x²y3-2y2
, the value of the last​

Answer 1

Answer:

Given,

x  

2

y  

3

=(x+y)  

5

 

Now taking logarithm with respect to the base e both sides we get,

2logx+3logy=5log(x+y)

Now differentiating both sides with respect to x we get,

x

2

​

+  

y

3

​

 

dx

dy

​

=  

x+y

5

​

(1+  

dx

dy

​

)

or, (  

x

2

​

−  

x+y

5

​

)=(  

x+y

5

​

−  

y

3

​

)  

dx

dy

​

 

or, (  

x(x+y)

2y−3x

​

)=(  

y(x+y)

2y−3x

​

)  

dx

dy   or,  

dx

dy

​

=  

x

y

​

.

Step-by-step explanation:

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