Solve (-10x^3)(-10x^3)(-10x^3)

$$( - 10 x ^ { 3 } ) ( - 10 x ^ { 3 } ) ( - 10 x ^ { 3 } )$$

Evaluate

$$-1000x^{9}$$

Solution Steps

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

$$-10x^{6}\left(-10\right)\left(-10\right)x^{3}$$

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

$$-10x^{9}\left(-10\right)\left(-10\right)$$

Multiply -10 and -10 to get 100.

$$100x^{9}\left(-10\right)$$

Multiply 100 and -10 to get -1000.

$$-1000x^{9}$$

Differentiate w.r.t. x

$$-9000x^{8}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10x^{6}\left(-10\right)\left(-10\right)x^{3})$$

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

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

Multiply -10 and -10 to get 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(100x^{9}\left(-10\right))$$

Multiply 100 and -10 to get -1000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-1000x^{9})$$

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

$$9\left(-1000\right)x^{9-1}$$

Multiply 9 times -1000.

$$-9000x^{9-1}$$

Subtract 1 from 9.

$$-9000x^{8}$$