Math Help - Total derivative

1. Total derivative

Find the total derivative dQ/dt, where Q = (x^2 + 4y^3) sin(2t^3), and x = t^3, y = t^2, expressing your final answer in terms of t alone (no x or y terms).

What is the value of dQ/dt?

2. $Q=(t^4+4t^6)sin(2t^3)$

$Q=t^4(1+4t^2)sin(2t^3)$

$\frac{dQ}{dt}=4t^3(1+4t^2)sin(2t^3)+8t^5sin(2t^3)+ 6t^6(1+4t^2)cos(2t^3)$

3. Originally Posted by mr_motivator
Find the total derivative dQ/dt, where Q = (x^2 + 4y^3) sin(2t^3), and x = t^3, y = t^2, expressing your final answer in terms of t alone (no x or y terms).

What is the value of dQ/dt?
Use

$\frac{dQ}{dt}=\frac{\partial Q}{\partial x}\frac{dx}{dt}+\frac{\partial Q}{\partial y}\frac{dy}{dt}$

and then substitute for $x$ and $y.$ Or substitute first and differentiate like normal.