Solve 24x^2ydiv(-6x)

$$24 x ^ { 2 } y \div ( - 6 x )$$

Evaluate

$$-4xy$$

Solution Steps

Cancel out 6x in both numerator and denominator.

$$\frac{4xy}{-1}$$

Anything divided by -1 gives its opposite.

$$-4xy$$

Differentiate w.r.t. x

$$-4y$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24y}{-6}x^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-4y\right)x^{1})$$

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}.

$$\left(-4y\right)x^{1-1}$$

Do the arithmetic.

$$\left(-4y\right)x^{0}$$

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

$$\left(-4y\right)\times 1$$

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

$$-4y$$