The question is as follows:
A rectangular lump of ice is melting under the sun. At time $t_0$ the lump has a height of 15 cm, length of 8 cm and width of 13 cm, and every one of the sizes is shrinking at a rate of 3 cm/hour (so derivatives of height, length and width as functions of time at the point $t_0$ are equal to $-3$). Find the derivative of volume with respect to time at point $t_0$ (so $\frac{dV}{dt}|_{t=t_0}$).
My thoughts are that we need to find a partial derivative of each individual measurement using the chain rule, then add them together and then plug in the values from the question. Volume is $w*h*l$.
So
$\frac{\partial V}{\partial t}=\frac{\partial V}{\partial w}\frac{\partial w}{\partial t}+\frac{\partial V}{\partial h}\frac{\partial h}{\partial t}+\frac{\partial V}{\partial l}\frac{\partial l}{\partial t} = -3*(\frac{\partial V}{\partial w} + \frac{\partial V}{\partial h} + \frac{\partial V}{\partial l}) = -3*(hl + wl + wh) = -3* (15*8 +13*8 +13*15) = -1257_{cm^3/hour}$
Is this correct? And am I using all the formulas correctly?