Solve x^2+1200sqrt{2}x-3*1200^2

$$x ^ { 2 } + 1200 \sqrt { 2 } x - 3 \times 1200 ^ { 2 }$$

Evaluate

$$x^{2}+1200\sqrt{2}x-4320000$$

Solution Steps

Calculate 1200 to the power of 2 and get 1440000.

$$x^{2}+1200\sqrt{2}x-3\times 1440000$$

Multiply 3 and 1440000 to get 4320000.

$$x^{2}+1200\sqrt{2}x-4320000$$

Differentiate w.r.t. x

$$2\left(x+600\sqrt{2}\right)$$

Steps Using Derivative Rule for Sum

Calculate 1200 to the power of 2 and get 1440000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+1200\sqrt{2}x-3\times 1440000)$$

Multiply 3 and 1440000 to get 4320000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+1200\sqrt{2}x-4320000)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2x^{2-1}+1200\sqrt{2}x^{1-1}$$

Subtract 1 from 2.

$$2x^{1}+1200\sqrt{2}x^{1-1}$$

Subtract 1 from 1.

$$2x^{1}+1200\sqrt{2}x^{0}$$

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

$$2x+1200\sqrt{2}x^{0}$$

For any term t except 0, t^{0}=1.

$$2x+1200\sqrt{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$2x+1200\sqrt{2}$$