Solve (8x^6)(4x^9)

$$( 8 x ^ { 6 } ) ( 4 x ^ { 9 } )$$

Evaluate

$$32x^{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 9 to get 15.

$$8x^{15}\times 4$$

Multiply 8 and 4 to get 32.

$$32x^{15}$$

Differentiate w.r.t. x

$$480x^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 9 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{15}\times 4)$$

Multiply 8 and 4 to get 32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(32x^{15})$$

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

$$15\times 32x^{15-1}$$

Multiply 15 times 32.

$$480x^{15-1}$$

Subtract 1 from 15.

$$480x^{14}$$