Solve -18x^2az^4/27x^5az

$$\frac { - 18 x ^ { 2 } a z ^ { 4 } } { 27 x ^ { 5 } a z }$$

Differentiate w.r.t. x

$$\frac{2z^{3}}{x^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{18az^{4}}{27az}\right)x^{2-5})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$2z^{3}x^{-4}$$

Evaluate

$$-\frac{2\times \left(\frac{z}{x}\right)^{3}}{3}$$

Solution Steps

Cancel out 9azx^{2} in both numerator and denominator.

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