Solve 12m^5-2m^2*3m^3

$$12 m ^ { 5 } - 2 m ^ { 2 } \times 3 m ^ { 3 }$$

Evaluate

$$6m^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$12m^{5}-2m^{5}\times 3$$

Multiply 2 and 3 to get 6.

$$12m^{5}-6m^{5}$$

Combine 12m^{5} and -6m^{5} to get 6m^{5}.

$$6m^{5}$$

Differentiate w.r.t. m

$$30m^{4}$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$5\times 12m^{5-1}+2\left(-6m^{3}\right)m^{2-1}$$

Multiply 5 times 12.

$$60m^{5-1}+2\left(-6m^{3}\right)m^{2-1}$$

Subtract 1 from 5.

$$60m^{4}+2\left(-6m^{3}\right)m^{2-1}$$

Multiply 2 times -2\times 3m^{3}.

$$60m^{4}+\left(-12m^{3}\right)m^{2-1}$$

Subtract 1 from 2.

$$60m^{4}+\left(-12m^{3}\right)m^{1}$$

For any term t, t^{1}=t.

$$60m^{4}+\left(-12m^{3}\right)m$$