Solve 2x^2*6x^2

$$2 { x }^{ 2 } \times 6 { x }^{ 2 }$$

Evaluate

$$12x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$2x^{4}\times 6$$

Multiply 2 and 6 to get 12.

$$12x^{4}$$

Differentiate w.r.t. x

$$48x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}\times 6)$$

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{4})$$

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

$$4\times 12x^{4-1}$$

Multiply 4 times 12.

$$48x^{4-1}$$

Subtract 1 from 4.

$$48x^{3}$$