Question

If u=x2y3, x=log t ,y=et find du/dt​

Answer 1

Answer:

U =(log t)^2e^3t

du/dt=(log t)^2(3e^3t)+e^3t(2)(log t)1/t

Answer 2

Step-by-step explanation:

u = x²y³

x = logt

y = e^t

du/dx = 2xy³

du/dy = 3x²y²

dx/dt = 1/t

dy/dt = e^t

du/dt = (du/dx)*(dx/dt) + (du/dy)*(dy/dt)

= 2xy³ * 1/t + 3x²y² * e^t

= xy²(2y/t + 3x*e^t)

= xy²(2y/t + 3xy)

= xy³(2/t + 3x)