Find dF/dr F=(GmM)/(r^2)

Problem

d()/d(r)(G*m*M)/(r2)

Solution

1. Identify the variables and constants in the expression. Since we are differentiating with respect to r the terms G m and M are treated as constants.

2. Rewrite the expression using a negative exponent to make it easier to apply the power rule.

(G*m*M)/(r2)=G*m*M*r(−2)

3. Apply the power rule for differentiation, which states that d(xn)/d(x)=n*x(n−1)

(d(G)*m*M*r(−2))/d(r)=G*m*M*(−2*r(−3))

4. Simplify the resulting expression by moving the variable with the negative exponent back to the denominator.

−2*G*m*M*r(−3)=−(2*G*m*M)/(r3)

Final Answer

d()/d(r)(G*m*M)/(r2)=−(2*G*m*M)/(r3)

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