Solve 4m*4m*m^2=

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

Evaluate

$$16m^{4}$$

Solution Steps

Multiply m and m to get m^{2}.

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

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

$$4m^{4}\times 4$$

Multiply 4 and 4 to get 16.

$$16m^{4}$$

Differentiate w.r.t. m

$$64m^{3}$$

Steps Using Definition of a Derivative

Multiply m and m to get m^{2}.

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

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

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

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}m}(16m^{4})$$

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

$$4\times 16m^{4-1}$$

Multiply 4 times 16.

$$64m^{4-1}$$

Subtract 1 from 4.

$$64m^{3}$$