u(1)+5, u'(1)=-7, v(1)=7, v'(1)=-3 d/dx(uv) at x=1

Answer: d/dx(uv) at x=1 = -67.

Explanation: The given information consists of the values of two functions, u(x) and v(x), and their derivatives, u'(x) and v'(x), at x=1. The task is to calculate the derivative of the product of these two functions at x=1, which is given by d/dx(uv) at x=1.

To solve this, we need to apply the product rule of differentiation, which states that if u(x) and v(x) are two functions, then the derivative of their product, uv, is given by d/dx(uv) = u'(x)v(x) + u(x)v'(x).

Given u(1)+5 = 6 and u'(1) = -7, v(1) = 7 and v'(1) = -3, we can substitute these values into the equation for d/dx(uv) and get:

d/dx(uv) at x=1 = u'(1)v(1) + u(1)v'(1)

d/dx(uv) at x=1 = -7 * 7 + 6 * -3

d/dx(uv) at x=1 = -49 + -18

d/dx(uv) at x=1 = -67

Therefore, d/dx(uv) at x=1 = -67.

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