Math Question and Answers


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
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
	$z=x^2 y+3xy^4 { ((x=sin2t)),((y=cost)) :}→(dz/dt)]_(t=0) =? z=4sin^2 tcos^3 t+6sintcos^5 t→(dz/dt)]_(t=0) = 4(2sintcos^4 t−3cos^2 tsin^3 t)+ 6(cos^5 t−5cos^4 tsin^2 t)= (0+0+0)+6(1−0)=6$
	$z = x^{2} y + 3 {x y}^{4}$ ${{\begin{cases} x = s i n 2 t \\ y = c o s t \end{cases} \to \frac{d z}{d t}]}_{t = 0} = ?$ ${z = 4 s i {\overset{2}{n t c o s}}^{3} t + 6 {s i n t c o s}^{5} t \to \frac{d z}{d t}]}_{t = 0} =$ $4 (2 {s i n t c o s}^{4} t - 3 {c o s}^{2} {t s i n}^{3} t) +$ $6 ({c o s}^{5} t - 5 {c o s}^{4} {t s i n}^{2} t) =$ $(0 + 0 + 0) + 6 (1 - 0) = 6$
	Answered by MM42 last updated on 24/Jan/24

	$\frac{d z}{d t} = \frac{d z}{d x} \times \frac{d x}{d t} + \frac{d z}{d y} \times \frac{d y}{d t}$ $= (2 x y + 3 y^{4}) \times 2 c o s 2 t + (x^{2} + 6 x y) (- s i n t)$ $t = 0 \Rightarrow \frac{d z}{d t} = 6 ✓$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum