Solve 5m^5(3m^2)

$$5 m ^ { 5 } ( 3 m ^ { 2 } )$$

Evaluate

$$15m^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$5m^{7}\times 3$$

Multiply 5 and 3 to get 15.

$$15m^{7}$$

Differentiate w.r.t. m

$$105m^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}m}(5m^{7}\times 3)$$

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}m}(15m^{7})$$

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

$$7\times 15m^{7-1}$$

Multiply 7 times 15.

$$105m^{7-1}$$

Subtract 1 from 7.

$$105m^{6}$$