Solve 1x^2*2x=

$$1 { x }^{ 2 } \times 2x=$$

Evaluate

$$2x^{3}$$

Solution Steps

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

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

Multiply 1 and 2 to get 2.

$$2x^{3}$$

Differentiate w.r.t. x

$$6x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(1x^{3}\times 2)$$

Multiply 1 and 2 to get 2.

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

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.

$$6x^{2}$$