Find `(dy)/(dx)` , when `x=a e^(theta)(sintheta-costheta),\ \ y=a e^(theta)(sintheta+costheta)`

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=ae^theta(sin theta + cos theta)`

Differentiating with respect to θ using uv rule which says that if u and v are some functions then (uv)’ = u’v + uv’

`Rightarrow frac{d y}{d theta}=a e^{theta}(sin theta+cos theta)+a e^{theta}(cos theta-sin theta)`



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