Solve frac{24x^{2}y^{3}z^4}{44x^4y^3z^2}=

$$\frac { 24 x ^ { 2 } y ^ { 3 } z ^ { 4 } } { 44 x ^ { 4 } y ^ { 3 } z ^ { 2 } } =$$

Differentiate w.r.t. x

$$-\frac{12z^{2}}{11x^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24y^{3}z^{4}}{44z^{2}y^{3}}x^{2-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6z^{2}}{11}x^{-2})$$

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}.

$$-2\times \frac{6z^{2}}{11}x^{-2-1}$$

Do the arithmetic.

$$\left(-\frac{12z^{2}}{11}\right)x^{-3}$$

Evaluate

$$\frac{6\times \left(\frac{z}{x}\right)^{2}}{11}$$

Solution Steps

Cancel out 4x^{2}z^{2}y^{3} in both numerator and denominator.

$$\frac{6z^{2}}{11x^{2}}$$