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Question
If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
Solution
x = sin θ
Differentiating w. r. t. θ, we get
`("d"x)/("d"theta) = "d"/("d"theta) (sintheta)` = cos θ
y = tan θ
Differentiating w. r. t. θ, we get
`("d"y)/("d"theta) = "d"/("d"theta) (tantheta)` = sec2 θ
∴ `("d"y)/("d"x) = ((("d"y)/("d"theta)))/((("d"x)/("d"theta))`
= `(sec^2theta)/(cos theta)`
= sec3 θ
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