Solve 4x*3x*12x^2

$$4x \times 3x \times 12 { x }^{ 2 }$$

Evaluate

$$144x^{4}$$

Solution Steps

Multiply x and x to get x^{2}.

$$4x^{2}\times 3\times 12x^{2}$$

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

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

Multiply 4 and 3 to get 12.

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

Multiply 12 and 12 to get 144.

$$144x^{4}$$

Differentiate w.r.t. x

$$576x^{3}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}\times 3\times 12x^{2})$$

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

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

Multiply 4 and 3 to get 12.

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

Multiply 12 and 12 to get 144.

$$\frac{\mathrm{d}}{\mathrm{d}x}(144x^{4})$$

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

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

Multiply 4 times 144.

$$576x^{4-1}$$

Subtract 1 from 4.

$$576x^{3}$$