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

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

Evaluate

$$10x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$2x^{10}\times 5$$

Multiply 2 and 5 to get 10.

$$10x^{10}$$

Differentiate w.r.t. x

$$100x^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{10}\times 5)$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{10})$$

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

$$10\times 10x^{10-1}$$

Multiply 10 times 10.

$$100x^{10-1}$$

Subtract 1 from 10.

$$100x^{9}$$