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

$$- x ^ { 3 } \times x ^ { 3 } \times ( - x ^ { 6 } )$$

Evaluate

$$x^{12}$$

Solution Steps

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

$$-x^{6}\left(-1\right)x^{6}$$

Multiply -1 and -1 to get 1.

$$x^{6}x^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$x^{12}$$

Differentiate w.r.t. x

$$12x^{11}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{6}\left(-1\right)x^{6})$$

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}x^{6})$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{12})$$

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

$$12x^{12-1}$$

Subtract 1 from 12.

$$12x^{11}$$