Solve (6x^3)(2x^7)

$$(6 { x }^{ 3 } )(2 { x }^{ 7 } )$$

Evaluate

$$12x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$6x^{10}\times 2$$

Multiply 6 and 2 to get 12.

$$12x^{10}$$

Differentiate w.r.t. x

$$120x^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{10}\times 2)$$

Multiply 6 and 2 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{10})$$

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

$$10\times 12x^{10-1}$$

Multiply 10 times 12.

$$120x^{10-1}$$

Subtract 1 from 10.

$$120x^{9}$$