Suppose that w = u(v) and u(0) = 2, v(0) = 3, u'(0) = 4, u'(3) = 5, v'(0) = 6, and v'(3) = 7. Find w'(0).

Question

Suppose that w = u(composition sign- little o)v and u(0) = 2, v(0) = 3, u'(0) = 4, u'(3) = 5, v'(0) = 6, and v'(3) = 7. Find w'(0).

Answer 1

w(x) = u[v(x)]
Use the chain rule to find the derivative of w
w'(x) = u'[v(x)]*v'(x)
Now plug in x = 0
w'(0) = u'[v(0)]*v'(0)
You are given that v(0) = 3 and v'(0) = 6, so plug those in
w'(0) = u'(3)*6
You are given that u'(3) = 5, so plug that in
w'(0) = 5*6
w'(0) = 30
Note: The problem is also throwing in some useless info just to confuse you. You don't need the values u(0), u'(0) or v'(3).

Answer 2

42