quick derivative question, i have answer, im just checking?

Question

Find y' if (x+y)^2 = (2x - y)^3

After all the calculations my answer was for the derivative is 2(x+y) - 3(2x - y)^2.

Now i did this with respect to y but now that i look at it i dont know if i was suppose to take the derivative with respect to x or y...any ideas?

or did it corrrectly

Answer 1

OK, whenever you do implicit differentiation, whenever you encounter the variable y, the derivative is always appended by the y'.

Also, do not forget chain rule:
Implicitly: 2(x+y)(1+y') - 3(2x - y)²(2-y') = 0
To get dy/dx = y', isolate y'.
2(x+y)(y') + 3(2x - y)²(y') = -2(x+y) + 6(2x - y)²

y' = [ -2(x+y) + 6(2x - y)² ] / [ 2(x+y) + 3(2x - y)² ]


d:

Answer 2

y' means dy/dx, so take the derivative with respect to x:

2*(x + y) * (1 + y') = 3*(2x - y)^2 * (2 - y')

solve for y'

Answer 3

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