Find dR/dM R=M^2(C/2-M/3)

Problem

d(R)/d(M)* where *R=M2*(C/2−M/3)

Solution

1. Distribute the M2 term into the parentheses to simplify the expression before differentiating.

R=(C*M2)/2−(M3)/3

2. Apply the power rule for differentiation, which states d(Mn)/d(M)=n*M(n−1) to each term separately.

d(R)/d(M)=d()/d(M)(C*M2)/2−d()/d(M)(M3)/3

3. Differentiate the first term, treating C as a constant.

d()/d(M)(C*M2)/2=C/2⋅2*M=C*M

4. Differentiate the second term.

d()/d(M)(M3)/3=1/3⋅3*M2=M2

5. Combine the results to find the final derivative.

d(R)/d(M)=C*M−M2

Final Answer

d(R)/d(M)=C*M−M2

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