If `x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e n` `y^(prime)(1)=4/3` (b) `y^(1)=-4/3` `y^(1)=-8(22)/(27)` (d) `y^(prime)(1)=2/3`

Options

A. `y'(1)=4//3`
B. `y''(1)=-4//3`
C. `y''(1)=-8(22)/(27)`
D. `y'(1)=2//3`

Explanation

To solve the problem, we need to differentiate the given equation implicitly and then evaluate the derivatives at the specified point. Let's go through the steps:

### Step 1: Differentiate the given equation implicitly
The given equation is:
\[ x^3 - 2x^2y^2 + 5x + y - 5 = 0 \]

Differentiating both sides with respect to \(x\):
\[
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