Solve 24x^2y^3z/18x^3yz^4

$$\frac { 24 x ^ { 2 } y ^ { 3 } z } { 18 x ^ { 3 } y z ^ { 4 } }$$

Differentiate w.r.t. x

$$-\frac{4\times \left(\frac{y}{x}\right)^{2}}{3z^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24zy^{3}}{18yz^{4}}x^{2-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4y^{2}}{3z^{3}}\times \frac{1}{x})$$

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}.

$$-\frac{4y^{2}}{3z^{3}}x^{-1-1}$$

Do the arithmetic.

$$\left(-\frac{4y^{2}}{3z^{3}}\right)x^{-2}$$

Evaluate

$$\frac{4y^{2}}{3xz^{3}}$$

Solution Steps

Cancel out 6yzx^{2} in both numerator and denominator.

$$\frac{4y^{2}}{3xz^{3}}$$