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Find dy/dx by implicit differentiation. Tan−1(5x2y) = x 4xy2.

Sagot :

tcchu2

Answer:

Differentiate both sides of the equation.

d

d

x

(

tan

-1

(

5

x

2

y

)

)

=

d

d

x

(

x

+

4

x

y

2

)

Differentiate the left side of the equation.

Tap for more steps...

(

x

2

d

d

x

[

y

]

+

2

y

x

)

5

1

+

25

x

4

y

2

Differentiate the right side of the equation.

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4

y

2

+

8

x

y

d

d

x

[

y

]

+

1

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

(

x

2

y

'

+

2

y

x

)

(

5

1

+

25

x

4

y

2

)

=

4

y

2

+

8

x

y

y

'

+

1

Solve for

y

'

.

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y

'

=

10

y

x

−

4

y

2

−

100

y

4

x

4

−

1

−

25

x

4

y

2

x

(

8

y

+

200

x

4

y

3

−

5

x

)

Replace

y

'

with

d

y

d

x

.

d

y

d

x

=

10

y

x

−

4

y

2

−

100

y

4

x

4

−

1

−

25

x

4

y

2

x

(

8

y

+

200

x

4

y

3

−

5

x

)

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