Solve (8x^7)(-3x^9)(5x^6)

$$( 8 x ^ { 7 } ) ( - 3 x ^ { 9 } ) ( 5 x ^ { 6 } )$$

Evaluate

$$-120x^{22}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 9 to get 16.

$$8x^{16}\left(-3\right)\times 5x^{6}$$

To multiply powers of the same base, add their exponents. Add 16 and 6 to get 22.

$$8x^{22}\left(-3\right)\times 5$$

Multiply 8 and -3 to get -24.

$$-24x^{22}\times 5$$

Multiply -24 and 5 to get -120.

$$-120x^{22}$$

Differentiate w.r.t. x

$$-2640x^{21}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 9 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{16}\left(-3\right)\times 5x^{6})$$

To multiply powers of the same base, add their exponents. Add 16 and 6 to get 22.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{22}\left(-3\right)\times 5)$$

Multiply 8 and -3 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-24x^{22}\times 5)$$

Multiply -24 and 5 to get -120.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-120x^{22})$$

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

$$22\left(-120\right)x^{22-1}$$

Multiply 22 times -120.

$$-2640x^{22-1}$$

Subtract 1 from 22.

$$-2640x^{21}$$