Solve x^4x^-2x=

$$x ^ { 4 } x ^ { - 2 } x =$$

Evaluate

$$x^{3}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{4}x^{-2}x^{1}$$

Use the Multiplication Rule for Exponents.

$$x^{4-2+1}$$

Add the exponents 4 and -2.

$$x^{2+1}$$

Add the exponents 2 and 1.

$$x^{3}$$

Differentiate w.r.t. x

$$3x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and -2 to get 2.

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

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

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

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

$$3x^{3-1}$$

Subtract 1 from 3.

$$3x^{2}$$