168k views
1 vote
Find dy/dx by implicit differentiation for her following equation. 4x + In y=x²y^6

User Gbozee
by
7.2k points

1 Answer

3 votes

Answer:

dy/dx = (2xy^7 - 4y) / (y - 6x^2y^6)

Explanation:

To find dy/dx by implicit differentiation, we differentiate both sides of the equation with respect to x.

Differentiating 4x + In y=x²y^6 with respect to x, we get:

4 + (1/y) dy/dx = 2xy^6 + 6x^2y^5 dy/dx

Now, we can isolate dy/dx by moving the terms that contain it to one side of the equation, and moving the rest to the other side:

(1/y - 6x^2y^5) dy/dx = 2xy^6 - 4

Dividing both sides by (1/y - 6x^2y^5), we get:

dy/dx = (2xy^6 - 4) / (1/y - 6x^2y^5)

Simplifying this expression, we can write:

dy/dx = (2xy^7 - 4y) / (y - 6x^2y^6)

User James Oravec
by
8.3k points