Solve x^3:(-x)

$$x ^ { 3 } : ( - x )$$

Differentiate w.r.t. x

$$-2x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{-1}x^{3-1})$$

Do the arithmetic.

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

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}.

$$2\left(-1\right)x^{2-1}$$

Do the arithmetic.

$$-2x^{1}$$

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

$$-2x$$

Evaluate

$$-x^{2}$$