Question

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.

uv at x = 1 dx
A) 36
B)-48
C)-32
D 48

Answer 1

To find the derivative of uv at x = 1, use the product rule and substitute the given values of u, v, and their derivatives into the equation.

Step-by-step explanation:

To find the derivative of uv at x = 1, we can use the product rule. The product rule states that the derivative of a product of two functions is equal to the derivative of the first function times the second function, plus the first function times the derivative of the second function.

In this case, u and v are differentiable functions of x, so we can write the derivative of uv as: d(uv)/dx = u * dv/dx + v * du/dx.

Given the values of u and v, and their derivatives, we can substitute these values into the equation to find the value of the derivative at x = 1.

So, d(uv)/dx at x = 1 = u(1) * v'(1) + v(1) * u'(1). Substitute the known values into this equation and calculate the result to get the answer.