# Differentiable functions of x

• carlarae
In summary, the problem asks to find the value of the derivative of the product of two differentiable functions u and v at x=1, given the values of u and v and their respective derivatives at the same point. Using the formula for the derivative of a product, the result is obtained by plugging in the given values and evaluating at x=1, resulting in a value of -53.

## 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

## The Attempt at a Solution

What have you tried?

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.

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?

carlarae said:
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

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.