Question

Ifz=u^2+V^2 and u=at^2, v=2at find dz /dt

Answer 1

Answer:

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

Step-by-step explanation:

$z=u^2+v^2\\z=(at^2)^2+(2at)^2\\z=a^2t^4+4a^2t^2\\\frac{dz}{dt} =a^2 \frac{d(t^4)}{dt} +4a^2\frac{d(t^2)}{dty} \\\frac{dz}{dt}=a^2 \times 4t^3+4a^2 \times 2t\\\frac{dz}{dt}=4a^2t^3+8a^2t\\\frac{dz}{dt}=4a^2t(t^2+2)$

Solution is $\frac{dz}{dt}=4a^2t(t^2+2)$