Suppose w=xy+yz, where x=e2t, y=2+sin(4t), and z=2+cos(7t).
a. use the chain rule to find dwdt as a function of x, y, z, and t. do not rewrite x, y, and z in terms of t, and do not rewrite e2t as x.
basically find the individual derivatives nd put it back into the mother derivative i.e dx/dt = 2e^2t dy/dt= 4cos 4t dZ/dt = -7sin 7t now from W=xy+yz dw/dx = y ( by partial differentiation) dw/dy= x+z dw/dz= y
now Dw/dt = ⅓{ (dx/dt×dw/dx) + (dy/dt×dw/dy)+(dz/dt×dw/dz)
