Solve (x)(x^5)(x)

$$( x ) ( x ^ { 5 } ) ( x )$$

Evaluate

$$x^{7}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{1}x^{5}x^{1}$$

Use the Multiplication Rule for Exponents.

$$x^{1+5+1}$$

Add the exponents 1 and 5.

$$x^{6+1}$$

Add the exponents 6 and 1.

$$x^{7}$$

Differentiate w.r.t. x

$$7x^{6}$$

Steps Using Definition of a Derivative

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

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

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

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

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

$$7x^{7-1}$$

Subtract 1 from 7.

$$7x^{6}$$