Solve (2x^4)(4x)

$$( 2 x ^ { 4 } ) ( 4 x )$$

Evaluate

$$8x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$2x^{5}\times 4$$

Multiply 2 and 4 to get 8.

$$8x^{5}$$

Differentiate w.r.t. x

$$40x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5}\times 4)$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{5})$$

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

$$5\times 8x^{5-1}$$

Multiply 5 times 8.

$$40x^{5-1}$$

Subtract 1 from 5.

$$40x^{4}$$