Finding the Value of a Derivative with Given Function and Derivative Values

[carlarae]

Homework Statement

Suppose u and v are differentiable functions of x. Use the given values of the functions and their derivatives to find the value of the indicated derivative.
u(1)=2, u'(1)=-7, v(1)=7,v'(1)=-2
d/dx (uv) at x =1

Homework Equations

The Attempt at a Solution

 

[gb7nash]

What have you tried?

 

[Simon Bridge]

Hint

Homework Equations

look for the equations you use when you have to differentiate a combination of two functions... one of them looks like your problem.

 

[carlarae]

I get d/x(uv)=(2)(-2) + (7)(-7) = -53 but I'm not applying the 1 anywhere that I know of here. as in u(1), does anyone have an example that could help me?

 

[Ray Vickson]

I get d/x(uv)=(2)(-2) + (7)(-7) = -53 but I'm not applying the 1 anywhere that I know of here. as in u(1), does anyone have an example that could help me?

In your answer (2)(2) + (7)(-7), where did the 2 come from? What about the -2? Where did you get the 7? Ditto for the -7.

RGV

 

[BrownianMan]

That answer looks correct to me. You are applying the 1. The equation for the derivative of the product of two functions is u*v' + v*u'. In your case, you have u(1)*v'(1) + v(1)*u'(1) = (2)(-2) + (7)(-7) = -53. This is d/dx(uv) evaluated at x=1.