Solve -6x^9*-3x^6

$$- 6 x ^ { 9 } \cdot - 3 x ^ { 6 }$$

Evaluate

$$18x^{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$-6x^{15}\left(-3\right)$$

Multiply -6 and -3 to get 18.

$$18x^{15}$$

Differentiate w.r.t. x

$$270x^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{15}\left(-3\right))$$

Multiply -6 and -3 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{15})$$

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

$$15\times 18x^{15-1}$$

Multiply 15 times 18.

$$270x^{15-1}$$

Subtract 1 from 15.

$$270x^{14}$$