Solve (5x^3)(3x^5)

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

Evaluate

$$15x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$5x^{8}\times 3$$

Multiply 5 and 3 to get 15.

$$15x^{8}$$

Differentiate w.r.t. x

$$120x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{8}\times 3)$$

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{8})$$

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

$$8\times 15x^{8-1}$$

Multiply 8 times 15.

$$120x^{8-1}$$

Subtract 1 from 8.

$$120x^{7}$$