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

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

Evaluate

$$-216x^{19}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$6x^{14}\left(-6\right)\times 6x^{5}$$

To multiply powers of the same base, add their exponents. Add 14 and 5 to get 19.

$$6x^{19}\left(-6\right)\times 6$$

Multiply 6 and -6 to get -36.

$$-36x^{19}\times 6$$

Multiply -36 and 6 to get -216.

$$-216x^{19}$$

Differentiate w.r.t. x

$$-4104x^{18}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{14}\left(-6\right)\times 6x^{5})$$

To multiply powers of the same base, add their exponents. Add 14 and 5 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{19}\left(-6\right)\times 6)$$

Multiply 6 and -6 to get -36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-36x^{19}\times 6)$$

Multiply -36 and 6 to get -216.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-216x^{19})$$

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

$$19\left(-216\right)x^{19-1}$$

Multiply 19 times -216.

$$-4104x^{19-1}$$

Subtract 1 from 19.

$$-4104x^{18}$$