Solve x*x*x*x

$$x \cdot x \cdot x \cdot x$$

Evaluate

$$x^{4}$$

Solution Steps

Multiply x and x to get x^{2}.

$$x^{2}xx$$

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

$$x^{3}x$$

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

$$x^{4}$$

Differentiate w.r.t. x

$$4x^{3}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

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

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

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

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

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

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

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

Subtract 1 from 4.

$$4x^{3}$$