Solve 6x^2y^3zdiv(-2xy)

$$6 x ^ { 2 } y ^ { 3 } z \div ( - 2 x y )$$

Evaluate

$$-3xzy^{2}$$

Solution Steps

Cancel out 2xy in both numerator and denominator.

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

Anything divided by -1 gives its opposite.

$$-3xzy^{2}$$

Differentiate w.r.t. x

$$-3zy^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6zy^{3}}{-2y}x^{2-1})$$

Do the arithmetic.

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

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}.

$$\left(-3zy^{2}\right)x^{1-1}$$

Do the arithmetic.

$$\left(-3zy^{2}\right)x^{0}$$

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

$$\left(-3zy^{2}\right)\times 1$$

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

$$-3zy^{2}$$