Solve 2x^2*x*x^3

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

Evaluate

$$2x^{6}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$2x^{6}$$

Differentiate w.r.t. x

$$12x^{5}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6})$$

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

$$6\times 2x^{6-1}$$

Multiply 6 times 2.

$$12x^{6-1}$$

Subtract 1 from 6.

$$12x^{5}$$