Solve x^2xxxxx

$${ x }^{ 2 } xxxxx$$

Evaluate

$$x^{7}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$x^{2}x^{1}x^{1}x^{1}x^{1}x^{1}$$

To multiply powers of the same base, add their exponents.

$$x^{2+1}x^{1+1}x^{1+1}$$

Add the exponents 2 and 1.

$$x^{3}x^{1+1}x^{1+1}$$

Add the exponents 1 and 1.

$$x^{3}x^{2}x^{1+1}$$

Add the exponents 1 and 1.

$$x^{3}x^{2}x^{2}$$

Differentiate w.r.t. x

$$7x^{6}$$

Steps Using Definition of a Derivative

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

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

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

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

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

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

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

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

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.

$$7x^{6}$$