Solve (-6x^6)(-5x^3)

$$( - 6 x ^ { 6 } ) ( - 5 x ^ { 3 } )$$

Evaluate

$$30x^{9}$$

Solution Steps

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

$$-6x^{9}\left(-5\right)$$

Multiply -6 and -5 to get 30.

$$30x^{9}$$

Differentiate w.r.t. x

$$270x^{8}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{9}\left(-5\right))$$

Multiply -6 and -5 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(30x^{9})$$

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

$$9\times 30x^{9-1}$$

Multiply 9 times 30.

$$270x^{9-1}$$

Subtract 1 from 9.

$$270x^{8}$$