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Question Number 69764 by Rio Michael last updated on 27/Sep/19

$$find\frac{dy}{dx}ifx={sin}^{2}tandy=tantatt=\frac{\pi }{4}$$

Commented by kaivan.ahmadi last updated on 27/Sep/19

$$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{1+{tan}^{2}t}{sin2t}$$

Answered by mind is power last updated on 27/Sep/19

$$\frac{dy}{dx}=\frac{dy}{dt}.\frac{dt}{dx}=\frac{dy}{dt}.{\left(\frac{dx}{dt}\right)}^{-1}=(1+{tg}^2\left(t\right)).{\left(sin\left(2t\right)\right)}^{-1}{\mid }_{t=\frac{\pi }{4}}=2.1^{-1}=2$$$$$$

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