Solve x^0*x*x^3

$${ x }^{ 0 } \times x \times { x }^{ 3 }$$

Evaluate

$$x^{4}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{0}x^{1}x^{3}$$

Use the Multiplication Rule for Exponents.

$$x^{1+3}$$

Add the exponents 1 and 3.

$$x^{4}$$

Differentiate w.r.t. x

$$4x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 0 and 1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}x^{3})$$

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

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

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

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

Subtract 1 from 4.

$$4x^{3}$$