Solve x*x^7*x^4

$$x \cdot x ^ { 7 } \cdot x ^ { 4 }$$

Evaluate

$$x^{12}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{1}x^{7}x^{4}$$

Use the Multiplication Rule for Exponents.

$$x^{1+7+4}$$

Add the exponents 1 and 7.

$$x^{8+4}$$

Add the exponents 8 and 4.

$$x^{12}$$

Differentiate w.r.t. x

$$12x^{11}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8}x^{4})$$

To multiply powers of the same base, add their exponents. Add 8 and 4 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.

$$12x^{11}$$