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

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

Evaluate

$$45x^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 5 to get 14.

$$5x^{14}\times 9$$

Multiply 5 and 9 to get 45.

$$45x^{14}$$

Differentiate w.r.t. x

$$630x^{13}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 5 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{14}\times 9)$$

Multiply 5 and 9 to get 45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(45x^{14})$$

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

$$14\times 45x^{14-1}$$

Multiply 14 times 45.

$$630x^{14-1}$$

Subtract 1 from 14.

$$630x^{13}$$