Solve 5x*2*10x*6

$$5 x \cdot 2 \cdot 10 x \cdot 6$$

Evaluate

$$600x^{2}$$

Solution Steps

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

$$5x^{2}\times 2\times 10\times 6$$

Multiply 5 and 2 to get 10.

$$10x^{2}\times 10\times 6$$

Multiply 10 and 10 to get 100.

$$100x^{2}\times 6$$

Multiply 100 and 6 to get 600.

$$600x^{2}$$

Differentiate w.r.t. x

$$1200x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}\times 2\times 10\times 6)$$

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{2}\times 10\times 6)$$

Multiply 10 and 10 to get 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(100x^{2}\times 6)$$

Multiply 100 and 6 to get 600.

$$\frac{\mathrm{d}}{\mathrm{d}x}(600x^{2})$$

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

$$2\times 600x^{2-1}$$

Multiply 2 times 600.

$$1200x^{2-1}$$

Subtract 1 from 2.

$$1200x^{1}$$

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

$$1200x$$