Solve (3x^6)(5x^7)

$$( 3 x ^ { 6 } ) ( 5 x ^ { 7 } )$$

Evaluate

$$15x^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 7 to get 13.

$$3x^{13}\times 5$$

Multiply 3 and 5 to get 15.

$$15x^{13}$$

Differentiate w.r.t. x

$$195x^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 7 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{13}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{13})$$

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

$$13\times 15x^{13-1}$$

Multiply 13 times 15.

$$195x^{13-1}$$

Subtract 1 from 13.

$$195x^{12}$$