Question

How do you us implicit differentiation to solve x( y + 2 )^5 = 8

x( y + 2 )^5 = 8

( y + 2 )^5 d/dx (x) + x d/dx(y+2)^5=d/dx 8

(y+2)^5 + 5x(y+2)^4 dy/dx=0

solve for dx/dy

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I assume you want dy/dx.
Differentiate both sides of the equation with respect to x. You do not have to solve explicity for y first.
(y+2)^5 + 5x (y+2)^4 *dy/dx= 0
dy/dx = -(y+2)/(5x)

Thanks.

Thanks.