Find the force of gravity ?! (Calculus) I have this problem in my Calculus book at the derivatives chapter but I do not know how to approach and solve this particular problem: > The mass of the earth is $5.983 \times 10^{24}$ kg. A meteorite with a mass of 10,000 kg is moving toward a collision with the earth. > > (a) When the meteorite is $100$ km from the earth, what is the force (in newtons) of gravitational attraction between the meteorite and the earth? > > (b) At that distance, how fast is this force increasing (in newtons per meter) as the meteorite continues on its collision course?

So I will assume you can plug in the numbers to obtain the solution for problem a. That being said, let's consider part b.

Since we're looking at the Force (F) with respect to the distance to the distance (r), let's take $\frac{dF}{dr}$. Do you understand why this is the derivative we want?

$r$ will be the variable in our problem since we are given $G, m_1,$ and $m_2$ and for the scope of this problem those will not change. So we will treat them as constants to take the derivative.

Performing the derivative, we obtain the following: $$\frac{dF}{dr} = Gm_1m_2\left(\frac{d}{dr}\frac{1}{r^2}\right)$$ This step utilizes the constant multiple rule of derivatives. We can then apply the power rule of derivatives to obtain the answer: $$\frac{dF}{dr} = \frac{-2Gm_1m_2}{r^3}$$

You should then be able to plug your constants and value for $r$ into the derivative formula to obtain an answer for part b.