# Find `del` w / `del` s by using the appropriate Chain Rule. w = x cos (yz), x = s2, y = t2, z = s - 5t

*print*Print*list*Cite

### 1 Answer

You need to find partial derivative `(del w)/(del s)` , hence, you need to differentiate the function `w = s^2cos(t^2(s - 5t))` with respect to s,using the product rule and the chain rule, such that:

`(del w)/(del s) = (del(s^2))/(del s)*cos(t^2(s - 5t)) + s^2*(del(t^2(s - 5t)))/(del s)`

`(del w)/(del s) = 2s*cos(t^2(s - 5t)) - s^2*sin(t^2(s - 5t))*(t^2)`

`(del w)/(del s) = 2s*cos(t^2(s - 5t)) - (s*t)^2*sin(t^2(s - 5t))`

**Hence, evaluating the partial derivative `(del w)/(del s)` , using the product rule and the chain rule, yields **`(del w)/(del s) = 2s*cos(t^2(s - 5t)) - (s*t)^2*sin(t^2(s - 5t)).`