Solve 10xquadtext{(9)}20x

$$10 x \quad \text { (9) } 20 x$$

Evaluate

$$1800x^{2}$$

Solution Steps

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

$$10x^{2}\times 9\times 20$$

Multiply 10 and 9 to get 90.

$$90x^{2}\times 20$$

Multiply 90 and 20 to get 1800.

$$1800x^{2}$$

Differentiate w.r.t. x

$$3600x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{2}\times 9\times 20)$$

Multiply 10 and 9 to get 90.

$$\frac{\mathrm{d}}{\mathrm{d}x}(90x^{2}\times 20)$$

Multiply 90 and 20 to get 1800.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1800x^{2})$$

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

$$2\times 1800x^{2-1}$$

Multiply 2 times 1800.

$$3600x^{2-1}$$

Subtract 1 from 2.

$$3600x^{1}$$

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

$$3600x$$