Solve 12x*42x

$$12x \times 42x$$

Evaluate

$$504x^{2}$$

Solution Steps

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

$$12x^{2}\times 42$$

Multiply 12 and 42 to get 504.

$$504x^{2}$$

Differentiate w.r.t. x

$$1008x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}\times 42)$$

Multiply 12 and 42 to get 504.

$$\frac{\mathrm{d}}{\mathrm{d}x}(504x^{2})$$

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

$$2\times 504x^{2-1}$$

Multiply 2 times 504.

$$1008x^{2-1}$$

Subtract 1 from 2.

$$1008x^{1}$$

For any term t, t^{1}=t.

$$1008x$$