Solve (3x^5)*(5x^12)

$$( 3 x ^ { 5 } ) \times ( 5 x ^ { 12 } )$$

Evaluate

$$15x^{17}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 12 to get 17.

$$3x^{17}\times 5$$

Multiply 3 and 5 to get 15.

$$15x^{17}$$

Differentiate w.r.t. x

$$255x^{16}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 12 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{17}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{17})$$

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

$$17\times 15x^{17-1}$$

Multiply 17 times 15.

$$255x^{17-1}$$

Subtract 1 from 17.

$$255x^{16}$$