find-dy-dx-if-x-sin-2-t-and-y-tan-t-at-t-pi-4-

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

f i n d \frac{d y}{d x} i f x = {s i n}^{2} t a n d y = t a n t a t t = \frac{π}{4}

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

\frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}} = \frac{1 + {t a n}^{2} t}{s i n 2 t}

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

\frac{d y}{d x} = \frac{d y}{d t} . \frac{d t}{d x} = \frac{d y}{d t} . {(\frac{d x}{d t})}^{- 1} = (1 + {t g}^{2} (t)) . {(s i n (2 t))}^{- 1} ∣_{t = \frac{π}{4}} = 2 . 1^{- 1} = 2