Solve -8x^2/12x

$$\frac { - 8 x ^ { 2 } } { 12 x }$$

Evaluate

$$-\frac{2x}{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-8\right)^{1}x^{2}}{12^{1}x^{1}}$$

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

$$\frac{\left(-8\right)^{1}x^{2-1}}{12^{1}}$$

Subtract 1 from 2.

$$\frac{\left(-8\right)^{1}x^{1}}{12^{1}}$$

Reduce the fraction \frac{-8}{12} to lowest terms by extracting and canceling out 4.

$$-\frac{2}{3}x^{1}$$

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

$$-\frac{2}{3}x$$

Differentiate w.r.t. x

$$-\frac{2}{3} = -0.6666666666666666$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{8}{12}\right)x^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{2}{3}x^{1})$$

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}.

$$-\frac{2}{3}x^{1-1}$$

Do the arithmetic.

$$-\frac{2}{3}x^{0}$$

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

$$-\frac{2}{3}$$