Solve x^3*x^2-1

$$x ^ { 3 } \cdot x ^ { 2 - 1 }$$

Evaluate

$$x^{4}$$

Solution Steps

Subtract 1 from 2 to get 1.

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

Calculate x to the power of 1 and get x.

$$x^{3}x$$

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

Subtract 1 from 2 to get 1.

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

Calculate x to the power of 1 and get x.

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

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.

$$4x^{3}$$