Solve 1999x^2-4999^2-1)x-1999

$$1999 x ^ { 2 } - 4999 ^ { 2 } - 1 ) x - 1999$$

Evaluate

$$1999x^{2}-24990002$$

Solution Steps

Calculate 4999 to the power of 2 and get 24990001.

$$1999x^{2}-24990001-1$$

Subtract 1 from -24990001 to get -24990002.

$$1999x^{2}-24990002$$

Differentiate w.r.t. x

$$3998x$$

Steps Using Derivative Rule for Sum

Calculate 4999 to the power of 2 and get 24990001.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1999x^{2}-24990001-1)$$

Subtract 1 from -24990001 to get -24990002.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1999x^{2}-24990002)$$

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}.

$$2\times 1999x^{2-1}$$

Multiply 2 times 1999.

$$3998x^{2-1}$$

Subtract 1 from 2.

$$3998x^{1}$$

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

$$3998x$$