Solve 2x^2:-x

$$2 x ^ { 2 } : - x$$

Evaluate

$$-2x$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}x^{2}}{-x^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{2^{1}x^{2-1}}{-1}$$

Subtract 1 from 2.

$$\frac{2^{1}x^{1}}{-1}$$

Divide 2 by -1.

$$-2x^{1}$$

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

$$-2x$$

Differentiate w.r.t. x

$$-2$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-2x^{0}$$

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

$$-2$$