Solve 24xyz^2/30x^2yz

$$\frac { 24 x y z ^ { 2 } } { 30 x ^ { 2 } y z }$$

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24yz^{2}}{30yz}x^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4z}{5}\times \frac{1}{x})$$

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}.

$$-\frac{4z}{5}x^{-1-1}$$

Do the arithmetic.

$$\left(-\frac{4z}{5}\right)x^{-2}$$

Evaluate

$$\frac{4z}{5x}$$

Solution Steps

Cancel out 6xyz in both numerator and denominator.

$$\frac{4z}{5x}$$