Solve xxxxxxxxxxxx

$$xxxxxxxxxxxx$$

Evaluate

$$x^{12}$$

Solution Steps

Multiply x and x to get x^{2}.

$$x^{2}xxxxxxxxxx$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{3}xxxxxxxxx$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{4}xxxxxxxx$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$x^{5}xxxxxxx$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$x^{6}xxxxxx$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$x^{7}xxxxx$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$x^{8}xxxx$$

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

$$x^{9}xxx$$

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$x^{10}xx$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$x^{11}x$$

To multiply powers of the same base, add their exponents. Add 11 and 1 to get 12.

$$x^{12}$$

Differentiate w.r.t. x

$$12x^{11}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}xxxxxxxxxx)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}xxxxxxxx)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}xxxxxxx)$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

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

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{7}xxxxx)$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8}xxxx)$$

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

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

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{10}xx)$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{11}x)$$

To multiply powers of the same base, add their exponents. Add 11 and 1 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.

$$12x^{11}$$