Question-203638

Question Number 203638 by thean0000 last updated on 24/Jan/24

Commented by thean0000 last updated on 24/Jan/24

h e l p m e

Commented by thean0000 last updated on 24/Jan/24

w h i c h o n e i s a n s w e r

Answered by esmaeil last updated on 24/Jan/24

z = x^{2} y + 3 {x y}^{4}

{{\begin{cases} x = s i n 2 t \\ y = c o s t \end{cases} \to \frac{d z}{d t}]}_{t = 0} = ?

{z = 4 s i {\overset{2}{n t c o s}}^{3} t + 6 {s i n t c o s}^{5} t \to \frac{d z}{d t}]}_{t = 0} =

4 (2 {s i n t c o s}^{4} t - 3 {c o s}^{2} {t s i n}^{3} t) +

6 ({c o s}^{5} t - 5 {c o s}^{4} {t s i n}^{2} t) =

(0 + 0 + 0) + 6 (1 - 0) = 6

Answered by MM42 last updated on 24/Jan/24

\frac{d z}{d t} = \frac{d z}{d x} \times \frac{d x}{d t} + \frac{d z}{d y} \times \frac{d y}{d t}

= (2 x y + 3 y^{4}) \times 2 c o s 2 t + (x^{2} + 6 x y) (- s i n t)

t = 0 \Rightarrow \frac{d z}{d t} = 6 ✓

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