Solve (2x^9)(3x^6)

$$( 2 x ^ { 9 } ) ( 3 x ^ { 6 } )$$

Evaluate

$$6x^{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$2x^{15}\times 3$$

Multiply 2 and 3 to get 6.

$$6x^{15}$$

Differentiate w.r.t. x

$$90x^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{15}\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{15})$$

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

$$15\times 6x^{15-1}$$

Multiply 15 times 6.

$$90x^{15-1}$$

Subtract 1 from 15.

$$90x^{14}$$