Question

(8) If z = u^2 + v^2 and u = at^2, v = 2 at, find dz/dt.​

Answer 1

Answer:

$\frac{dz}{dt} =(8at^{2} +2at^{4})\frac{da}{dt} +4(2at^{2}+2a^{2} t^{3} )$

Step-by-step explanation:

z = u^2 + v^2 and u = at^2, v = 2 at

By substitution,

z= 4$a^{2}t^{2}$+$a^{2}t^{4}$

Differentiate z with respect to t,

Here only used product rule to differentiate,

$\frac{dz}{dt}=4(2at^{2}\frac{da}{dt}+2a^{2}t) + (2at^{4}\frac{da}{dt}+4a^{2}t^{3})$

$\frac{dz}{dt} =(8at^{2} +2at^{4})\frac{da}{dt} +4(2at^{2}+2a^{2} t^{3} )$