Solve -6x^2y^2zdiv(1/2xy^2)

$$- 6 x ^ { 2 } y ^ { 2 } z \div ( \frac { 1 } { 2 } x y ^ { 2 } )$$

Evaluate

$$-12xz$$

Solution Steps

Cancel out xy^{2} in both numerator and denominator.

$$\frac{-6xz}{\frac{1}{2}}$$

Divide -6xz by \frac{1}{2} by multiplying -6xz by the reciprocal of \frac{1}{2}.

$$-6xz\times 2$$

Multiply -6 and 2 to get -12.

$$-12xz$$

Differentiate w.r.t. x

$$-12z$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-12z\right)x^{0}$$

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

$$\left(-12z\right)\times 1$$

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

$$-12z$$