If `xa n dy` are the sides of two squares such that `y=x-x^2` . Find the change of the area of second square with respect to the area of the first square.

Explanation

Let area of the first square `A_{1}=x^{2}`


And area of the second square `A_{2}=y^{2}`


Now `A_{1}=x^{2}` and `A_{2}=y^{2}=(x-x^{2})^{2}`


Differentiating both `{A}_{1}` and `{A}_{2}` w.r.t. `t`, we get


`frac{{dA}_{1}}{{dt}}=2 x cdot frac{{dx}}{{dt}}` and `frac{{dA} 2}{{dt}}=2(x-x^{2})(1-2 x) cdot frac{{dx}}{{dt}}`


`therefore frac{d A_{2}}{d_{A_{1}}}=frac{frac{d A_{2}}{d t}}{frac{d A_{1}}{c t}}`


`=frac{2(x-x^{2})(1-2 x) cdot frac{d x}{d t}}{2 x cdot frac{d x}{d t}}`


`=frac{x(1-x)(1-2 x)}{x}`


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