# Thread: Help - Partial Derivatives of f(x,y)

1. ## Help - Partial Derivatives of f(x,y)

Hi , can anyone help me with this problem please

(a) Find w''(t) if $\displaystyle w=x^2 y , x = e^-t , y=ln(t)$

i was able to do it for w'(t) easily

w'(t) = dw/dx dx/dt + dw/dy dy/dt

However i dont know how to do it for w''(t) in the same way as w'(t)

(b) Find w''(t) if $\displaystyle w=f(x,y) , x=e^t , y = 2t - 1$

w'(t) = df/dx dx/dt + df/dy dy/dt

w''(t) = ?!?!?!?!?!

Please i need a little bit of explanation on finding w''(t)

Thanks

2. Originally Posted by x7amoooodx
Hi , can anyone help me with this problem please

(a) Find w''(t) if $\displaystyle w=x^2 y , x = e^-t , y=ln(t)$

i was able to do it for w'(t) easily

w'(t) = dw/dx dx/dt + dw/dy dy/dt

However i dont know how to do it for w''(t) in the same way as w'(t)
$\displaystyle w'(t)=2xy x'(t) + x^2 y'(t)$

$\displaystyle w''(t)=\left[\frac{\partial}{\partial x} w'\right] x'+\left[\frac{\partial}{\partial y} w'\right] y'$

etc.

CB