Solve (5x^6)(-3x^3)(2x^9)

$$( 5 x ^ { 6 } ) ( - 3 x ^ { 3 } ) ( 2 x ^ { 9 } )$$

Evaluate

$$-30x^{18}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$5x^{9}\left(-3\right)\times 2x^{9}$$

To multiply powers of the same base, add their exponents. Add 9 and 9 to get 18.

$$5x^{18}\left(-3\right)\times 2$$

Multiply 5 and -3 to get -15.

$$-15x^{18}\times 2$$

Multiply -15 and 2 to get -30.

$$-30x^{18}$$

Differentiate w.r.t. x

$$-540x^{17}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{9}\left(-3\right)\times 2x^{9})$$

To multiply powers of the same base, add their exponents. Add 9 and 9 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{18}\left(-3\right)\times 2)$$

Multiply 5 and -3 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15x^{18}\times 2)$$

Multiply -15 and 2 to get -30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-30x^{18})$$

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

$$18\left(-30\right)x^{18-1}$$

Multiply 18 times -30.

$$-540x^{18-1}$$

Subtract 1 from 18.

$$-540x^{17}$$