Solve (2x)(5x^3)

$$( 2 x ) ( 5 x ^ { 3 } )$$

Evaluate

$$10x^{4}$$

Solution Steps

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

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

Multiply 2 and 5 to get 10.

$$10x^{4}$$

Differentiate w.r.t. x

$$40x^{3}$$

Steps Using Definition of a Derivative

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

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

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{4})$$

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

$$4\times 10x^{4-1}$$

Multiply 4 times 10.

$$40x^{4-1}$$

Subtract 1 from 4.

$$40x^{3}$$