Solve 12x^2*3x^2

$$12 { x }^{ 2 } \times 3 { x }^{ 2 }$$

Evaluate

$$36x^{4}$$

Solution Steps

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

$$12x^{4}\times 3$$

Multiply 12 and 3 to get 36.

$$36x^{4}$$

Differentiate w.r.t. x

$$144x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{4}\times 3)$$

Multiply 12 and 3 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{4})$$

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

$$4\times 36x^{4-1}$$

Multiply 4 times 36.

$$144x^{4-1}$$

Subtract 1 from 4.

$$144x^{3}$$