Solve (3x^5)(-8x^5)(4x^9)

$$( 3 x ^ { 5 } ) ( - 8 x ^ { 5 } ) ( 4 x ^ { 9 } )$$

Evaluate

$$-96x^{19}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$3x^{10}\left(-8\right)\times 4x^{9}$$

To multiply powers of the same base, add their exponents. Add 10 and 9 to get 19.

$$3x^{19}\left(-8\right)\times 4$$

Multiply 3 and -8 to get -24.

$$-24x^{19}\times 4$$

Multiply -24 and 4 to get -96.

$$-96x^{19}$$

Differentiate w.r.t. x

$$-1824x^{18}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{10}\left(-8\right)\times 4x^{9})$$

To multiply powers of the same base, add their exponents. Add 10 and 9 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{19}\left(-8\right)\times 4)$$

Multiply 3 and -8 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-24x^{19}\times 4)$$

Multiply -24 and 4 to get -96.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-96x^{19})$$

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

$$19\left(-96\right)x^{19-1}$$

Multiply 19 times -96.

$$-1824x^{19-1}$$

Subtract 1 from 19.

$$-1824x^{18}$$