Solve (-2x^6)(3x^9)

$$( - 2 x ^ { 6 } ) ( 3 x ^ { 9 } )$$

Evaluate

$$-6x^{15}$$

Solution Steps

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

$$-2x^{15}\times 3$$

Multiply -2 and 3 to get -6.

$$-6x^{15}$$

Differentiate w.r.t. x

$$-90x^{14}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{15}\times 3)$$

Multiply -2 and 3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{15})$$

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

$$15\left(-6\right)x^{15-1}$$

Multiply 15 times -6.

$$-90x^{15-1}$$

Subtract 1 from 15.

$$-90x^{14}$$