Solve (5x^2)(3x^7)

$$(5 { x }^{ 2 } )(3 { x }^{ 7 } )$$

Evaluate

$$15x^{9}$$

Solution Steps

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

$$5x^{9}\times 3$$

Multiply 5 and 3 to get 15.

$$15x^{9}$$

Differentiate w.r.t. x

$$135x^{8}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{9}\times 3)$$

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{9})$$

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

$$9\times 15x^{9-1}$$

Multiply 9 times 15.

$$135x^{9-1}$$

Subtract 1 from 9.

$$135x^{8}$$