Solve (7x*6)(3x*4)

$$(7x \times 6)(3x \times 4)$$

Evaluate

$$504x^{2}$$

Solution Steps

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

$$7x^{2}\times 6\times 3\times 4$$

Multiply 7 and 6 to get 42.

$$42x^{2}\times 3\times 4$$

Multiply 42 and 3 to get 126.

$$126x^{2}\times 4$$

Multiply 126 and 4 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}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}\times 6\times 3\times 4)$$

Multiply 7 and 6 to get 42.

$$\frac{\mathrm{d}}{\mathrm{d}x}(42x^{2}\times 3\times 4)$$

Multiply 42 and 3 to get 126.

$$\frac{\mathrm{d}}{\mathrm{d}x}(126x^{2}\times 4)$$

Multiply 126 and 4 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.

$$1008x$$