Solve (2x^3)(5x^3)

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

Evaluate

$$10x^{6}$$

Solution Steps

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

$$2x^{6}\times 5$$

Multiply 2 and 5 to get 10.

$$10x^{6}$$

Differentiate w.r.t. x

$$60x^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6}\times 5)$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{6})$$

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

$$6\times 10x^{6-1}$$

Multiply 6 times 10.

$$60x^{6-1}$$

Subtract 1 from 6.

$$60x^{5}$$