Question

Find d2y/dx2 if x4+y4=16

Answer 1

Answer:

Step-by-step explanation:

Differentiate both sides of the equation.

d

d

x

(

x

4

+

y

4

)

=

d

d

x

(

16

)

Differentiate the left side of the equation.

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4

x

3

+

4

y

3

d

d

x

[

y

]

Since  

16

is constant with respect to  

x

, the derivative of  

16

with respect to  

x

is  

0

.

0

Reform the equation by setting the left side equal to the right side.

4

x

3

+

4

y

3

y

'

=

0

Solve for  

y

'

.

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Subtract  

4

x

3

from both sides of the equation.

4

y

3

y

'

=

−

4

x

3

Divide each term by  

4

y

3

and simplify.

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y

'

=

−

x

3

y

3

Replace  

y

'

with  

d

y

d

x

.

d

y

d

x

=

−

x

3

y

3