Solve 2x^2*3x^8

$$2 { x }^{ 2 } \times 3 { x }^{ 8 }$$

Evaluate

$$6x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$2x^{10}\times 3$$

Multiply 2 and 3 to get 6.

$$6x^{10}$$

Differentiate w.r.t. x

$$60x^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{10}\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{10})$$

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

$$10\times 6x^{10-1}$$

Multiply 10 times 6.

$$60x^{10-1}$$

Subtract 1 from 10.

$$60x^{9}$$