Solve (2x^3)(9x^4)

$$( 2 x ^ { 3 } ) ( 9 x ^ { 4 } )$$

Evaluate

$$18x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$2x^{7}\times 9$$

Multiply 2 and 9 to get 18.

$$18x^{7}$$

Differentiate w.r.t. x

$$126x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{7}\times 9)$$

Multiply 2 and 9 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{7})$$

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

$$7\times 18x^{7-1}$$

Multiply 7 times 18.

$$126x^{7-1}$$

Subtract 1 from 7.

$$126x^{6}$$