Question

If eˣ−y=xy³e²−18, what is the value of dxdy​ at the point (2, 2)?

Answer 1

The value of dx/dy at the point (2,2) is -8e^2/7.

Step-by-step explanation:

To find the value of dx/dy at the point (2,2), we first need to differentiate the given equation e^x-y = xy^3e^2-18. Differentiating both sides with respect to x gives us:

e^x-y (dx/dy) = y^3e^2 - xy^3(dx/dy)

Substituting the values x=2 and y=2 into this equation, we can solve for dx/dy:

e^2-2 (dx/dy) = 2^3e^2 - 2(2)^3(dx/dy)

Simplifying, we get:

(1-8)(dx/dy) = 8e^2 - 16(dx/dy)

Combining similar terms, we can solve for dx/dy:

-7(dx/dy) = 8e^2

dx/dy = -8e^2/7