Solve 8x^3yzdiv(-2xyz)

$$8 x ^ { 3 } y z \div ( - 2 x y z )$$

Evaluate

$$-4x^{2}$$

Solution Steps

Cancel out 2xyz in both numerator and denominator.

$$\frac{4x^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$-4x^{2}$$

Differentiate w.r.t. x

$$-8x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8yz}{-2yz}x^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{2})$$

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}.

$$2\left(-4\right)x^{2-1}$$

Do the arithmetic.

$$-8x^{1}$$

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

$$-8x$$