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

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

Evaluate

$$45x^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$5x^{13}\times 9$$

Multiply 5 and 9 to get 45.

$$45x^{13}$$

Differentiate w.r.t. x

$$585x^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{13}\times 9)$$

Multiply 5 and 9 to get 45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(45x^{13})$$

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

$$13\times 45x^{13-1}$$

Multiply 13 times 45.

$$585x^{13-1}$$

Subtract 1 from 13.

$$585x^{12}$$