Find derivative problem
Find B’(6)

Step-by-step explanation:

We have:

And we want to find B’(6).

So, we will need to find B(t) first. To do so, we will take the derivative of both sides with respect to x. Hence:

We can move the constant outside:

Now, we will utilize the product rule. The product rule is:

We will let:

Then:

(The derivative of u was determined using the chain rule.)

Then it follows that:

Therefore:

By simplification:

So, the slope of the tangent line to the point (6, B(6)) is -28.17.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.