Solve (9x^4)(4x^5)

$$( 9 x ^ { 4 } ) ( 4 x ^ { 5 } )$$

Evaluate

$$36x^{9}$$

Solution Steps

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

$$9x^{9}\times 4$$

Multiply 9 and 4 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 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{9}\times 4)$$

Multiply 9 and 4 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.

$$324x^{8}$$