Solve (5x^2)(5x^7)

$$( 5 x ^ { 2 } ) ( 5 x ^ { 7 } )$$

Evaluate

$$25x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

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

Multiply 5 and 5 to get 25.

$$25x^{9}$$

Differentiate w.r.t. x

$$225x^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

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

Multiply 5 and 5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{9})$$

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

$$9\times 25x^{9-1}$$

Multiply 9 times 25.

$$225x^{9-1}$$

Subtract 1 from 9.

$$225x^{8}$$