Solve m^2*m^4+3(m^3)^2=

$$m ^ { 2 } \cdot m ^ { 4 } + 3 ( m ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$4m^{6}$$

Solution Steps

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

$$m^{6}+3\left(m^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

Combine m^{6} and 3m^{6} to get 4m^{6}.

$$4m^{6}$$

Differentiate w.r.t. m

$$24m^{5}$$

Steps Using Definition of a Derivative

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

Combine m^{6} and 3m^{6} to get 4m^{6}.

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

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

$$6\times 4m^{6-1}$$

Multiply 6 times 4.

$$24m^{6-1}$$

Subtract 1 from 6.

$$24m^{5}$$