Solve m^2m^4+m*m^3*m^2

$$m ^ { 2 } m ^ { 4 } + m \cdot m ^ { 3 } \cdot m ^ { 2 }$$

Evaluate

$$2m^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$m^{6}+mm^{3}m^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$m^{6}+m^{4}m^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$m^{6}+m^{6}$$

Combine m^{6} and m^{6} to get 2m^{6}.

$$2m^{6}$$

Differentiate w.r.t. m

$$12m^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{6}+mm^{3}m^{2})$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{6}+m^{4}m^{2})$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{6}+m^{6})$$

Combine m^{6} and m^{6} to get 2m^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(2m^{6})$$

The derivative of ax^{n} is nax^{n-1}.

$$6\times 2m^{6-1}$$

Multiply 6 times 2.

$$12m^{6-1}$$

Subtract 1 from 6.

$$12m^{5}$$