Find `(dy)/(dx)` , when `x=b\ sin^2theta` and `y=a\ cos^2theta`

Explanation

We can write `frac{d y}{d x} ` as

`frac{d y}{d x}=frac{frac{d y}{d theta}}{frac{d x}{d theta}}`....(i)

Let us first find `frac{d y}{d theta}`

We have `y=a cos^2 theta`

Differentiate with respect to θ

`Rightarrow frac{d y}{d theta}=a2cos theta (-sin theta)`
Now let us find `frac{d x}{d theta}`

We have `x=b sin^2 theta`
By differentiation

`Rightarrow frac{d x}{d theta}=b2sin theta cos theta`
Therefore

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