Solve (9x^5)(-3x^-2)

$$( 9 x ^ { 5 } ) ( - 3 x ^ { - 2 } )$$

Evaluate

$$-27x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and -2 to get 3.

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

Multiply 9 and -3 to get -27.

$$-27x^{3}$$

Differentiate w.r.t. x

$$-81x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and -2 to get 3.

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

Multiply 9 and -3 to get -27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-27x^{3})$$

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

$$3\left(-27\right)x^{3-1}$$

Multiply 3 times -27.

$$-81x^{3-1}$$

Subtract 1 from 3.

$$-81x^{2}$$