Solve 2x*2x^3=

$$2 x * 2 x ^ { 3 } =$$

Evaluate

$$4x^{4}$$

Solution Steps

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

$$2x^{4}\times 2$$

Multiply 2 and 2 to get 4.

$$4x^{4}$$

Differentiate w.r.t. x

$$16x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}\times 2)$$

Multiply 2 and 2 to get 4.

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

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

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

Multiply 4 times 4.

$$16x^{4-1}$$

Subtract 1 from 4.

$$16x^{3}$$