Question

Suppose that u and v are differentiable at functions of x, use the given values of the functions and their derivitaves to find the value of the indicated deriv.

u(1)= 5, u'(1)=-5, v(1)=6, v'(1)=-2

Answer 1

the derivative of a function f(u,v) is equal to d/du f(u,v) * u'(t)+ d/dv f(u,v) * v'(t)
at time t=1, this is equal to
d/du f(5,6) * (-5) + d/dv f(5,6) * (-2)

Answer 2

if f(u,v)=u*v, then d/du f(u,v)=v and d/dv f(u,v)=u
6*(-5)+5*(-2)

Answer 3

which is just the product rule