Solve 3xx^2-x^2x

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

Evaluate

$$2x^{3}$$

Solution Steps

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

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

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

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

Combine 3x^{3} and -x^{3} to get 2x^{3}.

$$2x^{3}$$

Differentiate w.r.t. x

$$6x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}-x^{2}x)$$

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

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

Combine 3x^{3} and -x^{3} to get 2x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3})$$

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

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

Multiply 3 times 2.

$$6x^{3-1}$$

Subtract 1 from 3.

$$6x^{2}$$