Solve (12x^3)*(4x)

$$( 12 x ^ { 3 } ) \cdot ( 4 x )$$

Evaluate

$$48x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

Multiply 12 and 4 to get 48.

$$48x^{4}$$

Differentiate w.r.t. x

$$192x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

Multiply 12 and 4 to get 48.

$$\frac{\mathrm{d}}{\mathrm{d}x}(48x^{4})$$

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

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

Multiply 4 times 48.

$$192x^{4-1}$$

Subtract 1 from 4.

$$192x^{3}$$