Verified answer

x^9 + y^2 = √5

By implicit differentiation:

9x^8 + 2y(dy/dx) = 0

2y(dy/dx) = -9x^8

dy/dx = (-9/2)(x^8 / y)

x^9+y^2=√5

1. 9x^8 + 2y (dy/dx) = 0

Differentiate the first term by power rule. The second term must be differentiated implicitly, that is, whenever you differentiated y, it must be followed by dy/dx. The derivative of a constant is zero.

2. 2y (dy/dx)= -9x^8

Transpose the first term to the right.

3. (dy/dx)= -9x^8/2y

Solve dy/dx

I hope this would help...

x^9+y^2=√5

y^2 = -x^9 + sqrt (5)

2y dy = -9x^8 dx + 0

dy/dx = (-9x^8) / (2y)

derivatives huh??

dy/dx is equal to y'(y prime) or f'(x)(f prime of x)

so..x^9+x^2=5^1/2

y^2=(5^1/2-x^9)

y=(5^1/2-x^9)^1/2

y=1/2(5^1/2-x^9)^-1/2

y'=1/[1/2(5^1/2-x^9)]--continue to simplify

y = root(x^5 - x^9)

dy/dx = (5x^4 - 9x^8)*1/2(x^5 - x^9) ^(-1/2)