Solve m^5*3m^3*2m^4=

$$m ^ { 5 } \times 3 m ^ { 3 } \times 2 m ^ { 4 } =$$

Evaluate

$$6m^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$m^{8}\times 3\times 2m^{4}$$

To multiply powers of the same base, add their exponents. Add 8 and 4 to get 12.

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

Multiply 3 and 2 to get 6.

$$m^{12}\times 6$$

Differentiate w.r.t. m

$$72m^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{8}\times 3\times 2m^{4})$$

To multiply powers of the same base, add their exponents. Add 8 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{12}\times 3\times 2)$$

Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{12}\times 6)$$

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

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

Multiply 12 times 6.

$$72m^{12-1}$$

Subtract 1 from 12.

$$72m^{11}$$