Solve (2x^2)(3x^3)(6x^4)

$$( 2 x ^ { 2 } ) ( 3 x ^ { 3 } ) ( 6 x ^ { 4 } )$$

Evaluate

$$36x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$2x^{5}\times 3\times 6x^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$2x^{9}\times 3\times 6$$

Multiply 2 and 3 to get 6.

$$6x^{9}\times 6$$

Multiply 6 and 6 to get 36.

$$36x^{9}$$

Differentiate w.r.t. x

$$324x^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5}\times 3\times 6x^{4})$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{9}\times 3\times 6)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{9}\times 6)$$

Multiply 6 and 6 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{9})$$

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

$$9\times 36x^{9-1}$$

Multiply 9 times 36.

$$324x^{9-1}$$

Subtract 1 from 9.

$$324x^{8}$$