Solve 9x(-3x^8)

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

Evaluate

$$-27x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

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

Multiply 9 and -3 to get -27.

$$-27x^{9}$$

Differentiate w.r.t. x

$$-243x^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

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

Multiply 9 and -3 to get -27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-27x^{9})$$

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

$$9\left(-27\right)x^{9-1}$$

Multiply 9 times -27.

$$-243x^{9-1}$$

Subtract 1 from 9.

$$-243x^{8}$$